Non-destructive testing of photon qubits | Nature

2021-11-25 11:58:06 By : Ms. Jean Tan

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Nature vol. 591, pages 570–574 (2021) cite this article

One of the biggest challenges of experimental quantum information is to maintain the fragile superposition state of qubits. The material qubit carrier can achieve a long life as the memory 2, at least in principle, but it cannot be used to propagate photons 3 that are quickly lost due to absorption, diffraction, or scattering. The loss problem can be alleviated by a lossless photon qubit detector, which predicts photons without destroying the coded qubit. It is envisaged that such detectors can facilitate protocols where distributed tasks rely on the successful propagation of photon qubits4,5, improve loss-sensitive qubit measurements6,7 and enable certain quantum key distribution attacks8. Here, we show this detector based on a single atom in two crossed fiber optic resonators, one for qubit-insensitive atom-photon coupling, and the other for atomic state detection9. We have achieved non-destructive testing with a qubit survival rate of 79±3% and a photon survival probability of 31±1%, and we have retained the qubit information with a fidelity of 96.2±0.3%. To illustrate the potential of our detector, we show that compared with previous methods, it can improve the rate and fidelity of long-distance entanglement and quantum state distribution under current parameters, and provide resource optimization and enable detection through qubit amplification. Vulnerability-Free Bell Test.

Qubit is the basic information unit in quantum information science. Two modes of encoding a qubit into a single photon can realize the long-distance distribution of quantum information. This makes a series of experiments possible, from basic tests of quantum physics10,11 to applications related to quantum communication3 and quantum networks9,12. However, the inevitable absorption, diffraction and scattering losses of long transmission channels severely limit the transmission distance. It should be emphasized that the occurrence of these losses is usually independent of the state of the qubits encoded in the two optical modes, whether it is time bins or light polarization. In fact, in optical fibers, the loss rate of the qubit carrier (photon) may be many orders of magnitude greater than the overall decoherence rate of the encoded qubit. In contrast, material qubit carriers are rarely lost in any quantum information protocol demonstrated so far. For photons, loss is fundamental and cannot be eliminated in any envisioned quantum information processing task. However, as long as there is a lossless photon qubit detector (NPQD), the loss effect can be mitigated by tracking the photon without destroying the encoded qubit.

Once in hand, such an NPQD can communicate with the sending and receiving nodes of the quantum network, regardless of whether the photon qubit is lost in the process (Figure 1a). This loss monitoring has several advantages: First, when the photon carrying the qubit is found to be lost along the communication channel, it allows the quantum communication scheme to stop the execution of further operations and restart the protocol. This is important when these operations are time-consuming or involve the use of valuable resources such as long-distance entanglement for quantum teleportation. Second, the detector can pre-authenticate the arrival of the photon qubit immediately before the planned quantum measurement, so that the latter only occurs when the qubit is present at the measurement input. This allows us to perform loss-sensitive qubit measurements even in the presence of high transmission losses. Examples include measurements that are limited by detection noise, photon receiving repeater scheme 13, or experiments where qubit loss leads to loopholes in Bell Tests 6 and 7. The last point is crucial for device-independent quantum key distribution.

a, a quantum network containing NPQD. Detected and undetected qubit photon events are shown in green and red, respectively. b. The NPQD setting shows the cross-fiber cavity together with the microwave antenna and the status detection beam (solid red line). The input photon qubit (red arrow) is reflected by the NPQD through a high-transmission non-polarizing beam splitter (NPBS, reflectivity R = 0.5%), and then sent to the qubit measurement device (black dotted rectangle), including λ /2 and λ/ 4 wave plates, polarizing beam splitter (PBS) and single photon detector (SPD). c, atomic level scheme and qubit coupling transition (dashed arrow). d. The atomic state affects the qubit photon entering the qubit cavity. |ea⟩ represents the excited state of the atom coupled to |0a⟩ through the qubit cavity mode. e, Bloch spheres I-IV show the atomic states at different stages of the ideal NPQD scheme.

Although recent progress has been made in the quantum non-destructive detection of light and microwave fields 15, 16, 17, 18, 19, 20, 21, the non-destructive detection of photon energy without projecting encoded qubit information is still an important issue. Outstanding challenges. Some work related to the experimental implementation of NPQD in the optical domain has been carried out, such as the non-destructive detection of bright dual-mode optical pulses using cross-phase modulation22, although this scheme is far from the single-photon qubit mechanism. Another method utilizes the parameter down-conversion of the incoming qubit photons, where one down-converted photon indicates the existence of the qubit, and the other provides the qubit information. Due to the low conversion efficiency of the applied photon splitting process, this method shows a severely limited efficiency (-76 dB). Other related work includes pioneer qubit amplifiers, which use two auxiliary photons 24 that interfere with the input signal. However, interference requires prior knowledge about pulse shape and arrival time, thus limiting the range of possible applications. Finally, our previous work on Omen Quantum Memory 25, 26 can be combined with readout for Omen photon qubits. However, the single-photon precursor signal is highly sensitive to loss, so the detection efficiency of the system is low. It is important to point out (compared to the NPQD reported here) that all the qubit pioneers mentioned will destroy the original incoming photon waveform, which is important in applications where synchronization and interference are important, such as time bin qubits Or linear optical quantum computing 27.

Here we demonstrate the implementation of NPQD that uses a single atom to strongly couple the modes of two independent optical resonators. The photon-polarized qubits are sent to the qubit cavity, where they are reflected while leaving a π phase shift in the atomic superposition state. Through coherent operations on atomic superposition states, the phase information is mapped into population information, which can be read out using the state detection cavity. This signal indicates the non-destructive detection of photon qubits reflected from the qubit cavity. We show that the strong atom-photon interaction provided by the two cavities allows for effective NPQD. We also proved that the reflection mechanism preserves the time waveform of the light pulse, which is essential for photon time bin qubits.

The qubit-atom interaction mechanism is essentially a monorail version of the scheme proposed by Duan et al.28. In our example, it starts with an 87Rb atom, in the state \((|{0}_{{\rm{a}}}\rangle |{1}_{{\rm{a}}}\ rangle) /\sqrt{2}\) (Bloch sphere I in Figure 1e). The atomic state |0a⟩ is strongly coupled with the cavity mode, thereby preventing photons from entering the cavity. Instead, photons are reflected from the cavity input mirror (Figure 1d), making |Ψph⟩ |0a⟩ → |Ψph⟩ |0a⟩, where |Ψph⟩ represents the photon polarization qubit. In contrast, the state |1a⟩ has no transition that resonates with the qubit cavity. Therefore, the qubit photon enters the cavity and obtains a π phase shift when reflected, |Ψph⟩ |1a⟩ → −|Ψph⟩ |1a⟩. Together, the qubit photon flips the atomic superposition state into \((|{0}_{{\rm{a}}}\rangle -|{1}_{{\rm{a}}}\rangle )/\ sqrt{2}\) (Bloch Sphere II). Finally, in the case of a (no) qubit photon (Bloch Sphere III), the π/2 pulse rotates the atomic state to |0a⟩ (|1a⟩ ), enabling us to pass deterministic atom-state detection ( Bloch Sphere IV).

Compared with previous experiments, our scheme is realized by two key factors: First, we choose a state |0a⟩ ≔ |F = 1, mF = 0⟩ so that the qubit cavity has two left and right circular polarizations and frequencies − Degenerate eigenmode, strongly coupled with two atomic transitions, |0a⟩ ↔ |F' = 2, mF = ±1⟩ (Figure 1c). Here, F and F'represent the magnitude of the total atomic angular momentum, and mF represents their projection on the quantization axis. By definition, the coupling strength of the two transitions is equal, but much smaller than the cyclic transition. We compensate for this reduction by using miniaturized fiber resonators to achieve the synergy of coupling constant g = 2π × (18.6 ± 0.5) MHz and C = 1.67 ± 0.09 (see method). Second, the compact lateral size of the fiber resonator allows the integration of a second crossed fiber resonator with a small mode volume. Here, it is used as a state detection cavity, tuned to the atomic cycle transition |F = 2⟩ ↔ |F′ = 3⟩, so that a strong fluorescence signal can be observed from |1a⟩ ≔ |F = 2, mF = 0⟩ This is used to distinguish the two atomic states |0a⟩ and |1a⟩, with a fidelity of (98.2 ± 0.2)% and a photon threshold of 1.

The physical elements required to implement NPQD are shown in Figure 1b. The photon qubit |Ψph⟩ first passes through a high-transmission non-polarizing beam splitter. Although the non-polarizing beam splitter is suitable for characterization measurements using weakly coherent pulses, it should be replaced by an efficient optical circulator for future implementations using single photons (Figure 1a). After reflection at the non-polarizing beam splitter, the photon qubits are coupled into a single-mode fiber, which is connected to the qubit fiber cavity where non-destructive interaction occurs. The reflected qubit photons are characterized by state tomography. The coherent manipulation of the atomic ground state is achieved by the microwave field emitted by the antenna close to the fiber cavity. The microwave flips the atomic state with a probability of (97 ± 1)% within approximately 12 μs (see method). The detector precursor signal is generated by a laser, which, together with the state detection cavity, induces cavity-enhanced fluorescence within a typical 7.5 μs9. Fluorescent photons are mainly emitted into the cavity, from where they are directed to the single-photon detector. Note that both fiber cavities are single-sided (see Reference 26 for details), so the main escape channels for cavity photons are two single-mode fibers.

We now describe the non-destructive detection of photon polarization qubits. To this end, a single-photon-level weak coherent pulse is used. Figure 2a illustrates the NPQD time series by showing the qubit measurement setup and the time histogram of the single-photon detector count output from the state detection cavity. The average number of photons here is |α|2 = 0.13 in front of the qubit cavity. It can be seen that the reflection of photon qubits at NPQD (green bars) has a great influence on the number of observed state detection photons (red bars) compared to the case where qubits are not sent (blue bars). This can effectively detect photon qubits. However, the definition of NPQD efficiency is unclear because it depends on the use case. Related parameters related to the efficiency of NPQD include the conditional probability of detecting atoms in the qubit precursor state |0a⟩, or given a qubit at the qubit cavity output (1oq), P(0a|1oq) = (79 ± 3 )%, or given a qubit at the NPQD input (1iq), P(0a|1iq) = (45 ± 2)%, photon survival probability ηsurv = (31 ± 1)%. Another advantage of any detector is the dark count probability. For our NPQD, it is pDC = (3.3 ± 0.2)%.

a. Shows the time histogram of the NPQD sequence, which includes microwave pulses, reflected qubit photon events (green), and state detection photon events. The red (blue) state detection count represents data conditioned on the detection of reflected photon qubits (no incoming photon qubits). Labels I-IV refer to the Bloch sphere in Figure 1e. b. The Poincaré sphere shows the results of the non-destructively detected reflected photon qubit state tomography (color sphere). The label indicates input polarization. c, Average fidelity\({\bar{ {\mathcal F} }}_{x}\) and a bar graph of quantum process state fidelity\({\bar{ {\mathcal F} }}_ {{\rm {s}},\chi }\). The Poincaré sphere shows the rotation around the A/D axis, and if eliminated, it will result in \({​​\bar{ {\mathcal F} }}_{\circlearrowleft }\). d. Test the retention of photon waveforms by reflecting photon qubits with three different waveforms from the NPQD (blue dot). The yellow dot indicates the measured value of the cavity as a reference. The error bars in c (d) describe the 1σ confidence interval (standard deviation). The error bars of \({\bar{ {\mathcal F} }}_{{\rm{s}},\chi }\) are evaluated by Monte Carlo method and represent standard errors.

Since NPQD should retain qubits, the outgoing photon qubits are scanned with polarization state and compared with the incoming qubits. Using this we calculate the fidelity \( {\mathcal F} \) = ⟨Ψin|ρout|Ψin⟩. A tomography scan of six orthogonal polarization states (Figure 2b) shows that \({\bar{ {\mathcal F} }}_{{\rm{a}}{\rm{l}}{ \rm {l}}}=(96.2\pm 0.3){\rm{ \% }}\) Subject to lossless qubit detection. Our fidelity, here |α|2 = 0.2, greatly exceeds the upper limit of fidelity 2/3 or 5/6, which is possible for the scheme of using 1 → ∞ or 1 → 2 universal quantum cloning machine, respectively Of 30. Note that due to the higher photon contribution of weakly coherent pulses, the limit must be moved slightly to 67.5% (Reference 31) and 84.9%. In this context, we conclude that our NPQD operates in a quantum mechanism.

The main contribution to the distortion comes from the polarization rotation around the A/D axis, due to the residual birefringence of the qubit cavity (see methods). The average fidelity of the rotated and non-rotated states is determined by \({\bar{ {\mathcal F} }}_{{\rm{HVRL}}}\) and \({\bar{ {\mathcal F} }} _{{\rm{AD}}}\), respectively (Figure 2c). However, taking this rotation into account in the calculation (which is experimentally feasible by placing a retardation wave plate after the qubit cavity) leads to \({​​\overline{ {\mathcal F} }}_{\circlearrowleft }= (98.0\pm 0.3) \% \) (orange bar). The remaining 2% of infidelity is due to errors in the calibration of the qubit measurement settings and fluctuations in the resonance frequency of the qubit cavity. In addition, through the maximum likelihood fitting to reconstruct the quantum process, the overall average state fidelity is \({\bar{ {\mathcal F} }}_{{\rm{s}},\chi }=( 96.3\ 0.6)\%\) in the afternoon.

Another important feature of NPQD is to retain the time waveform of photon qubits (Figure 2d). This is very important in cases where photon interference or quantum information is encoded in the time pattern of photons, in addition to or instead of polarization. To show that our NPQD retains the waveform, we compared the three different envelopes (blue dots) of the qubit pulse reflected by the atom-cavity system with the pulse reflected by the cavity (yellow dot). For all three cases, we found that the intensity waveforms between the outgoing photon and the incoming photon overlap more than 99.5%.

The average number of input photons of the weakly coherent pulse of the encoding qubit |α|2 has an impact on the performance of the NPQD. Its characteristics are shown in Figure 3, which shows the different quality factors of our detector. For a given range |α|2 in front of the qubit cavity, the non-destructive detection probability of qubit survival P(0a|≥1oq) (blue dot in Figure 3a) shows the maximum value at | at (79±3)%. α|2 = 0.13. Here, the main error is due to the difference in the reflection coefficient of the coupling strength \(({R}_{|{0}_{{\rm{a}}}\rangle }=0.50\pm 0.02)\) and a non- Coupling atom\(({R}_{|{1}_{{\rm{a}}}\rangle }=0.117\pm 0.003)\); see method. For high |α|2, due to the balanced contribution of 32 odd and even photons, the conditional probability converges to 0.5, and due to the dark count set by the qubit measurement, the conditional probability will decrease the value of |α|2. The unconditional probability P(0a) (green dot) shows the same convergence for high |α|2. However, within the limit of |α|2 → 0, the probability is lower bound by pDC (gray dashed line), which is due to defects in atomic state manipulation, optical pumping, and state detection.

a, the probability of non-destructive detection as a function of the average number of photons input in front of the qubit cavity |α|2. P(0a|≥1oq) is conditional on successful qubit reflection (≥1oq), while P(0a) is unconditional. The horizontal dashed line represents the NPQD dark count probability pDC. b, The average number of photons output by the qubit cavity under the condition of non-destructive testing events\({\bar{n}}_{{\rm{oq}}}({0}_{{\rm{a}}} ) \). Inset, the autocorrelation function g(2) (τ = 0) of the qubit detected by the non-destructive test. All solid data points adopt Gaussian photon pulse shape and linear near-vertical polarization. Use orthogonal polarization (different pulse shapes; Figure 2c) to obtain hollow circle (square) data points. For all figures, the solid line is given by the theoretical simulation described in the supplementary information. The dotted line in b considers pDC = 0. The error bars in a represent the 1σ confidence interval. The error bars in b and the inset in b represent standard errors and standard deviations, respectively.

Another important quality factor is the probability of having photon qubits at the output of NPQD, and its condition is its non-destructive detection P(1oq|0a). Because we use weak coherent states (rather than single-photon Fock states) to characterize NPQD, we show the conditional average photon number in Figure 3b. \({\bar{n}}_{{\rm{oq} }}( {0}_{{\rm{a}}})\), for small input photons, it is equivalent to P(1oq|0a). We observe that \({\bar{n}}}_{{\rm{oq}}}({0}_{{\rm{a}}})=0.56\pm 0.02\) for |α|2 = 0.2, but due to NPQD dark count pDC, this value will decrease with smaller |α|2. Consider the simulation with pDC = 0 (dashed line), which converges to P(1oq|0a) = 52.3% when |α|2 → 0. Due to the parasitic loss of the cavity mirror, imperfect mode matching and a finite atomic decay rate. Interestingly, not only the average photon count but also the photon statistics will change after the qubit is reflected (Figure 3b, inset). We prove this by measuring the second-order autocorrelation function of the reflection qubit at zero time delay g(2)(0), which is conditioned on non-destructive detection. The sub-Poisson statistics obtained g(2)(0) <1 are derived from the extraction of single photons from incoming weakly coherent pulses (see Supplementary Information and Reference 32).

To explore the potential of our NPQD, we will now discuss four example applications (details in the method) that will benefit from our detector. Figures 4a and b illustrate how monitoring qubit loss along the transmission channel saves time and valuable resources. The first example (Figure 4a) consists of an atom-photon entanglement source 9, which sends photon qubits to a predictive quantum memory 26 to generate sender-receiver entanglement. The figure shows the entanglement acceleration, defined as the ratio of the average entanglement generation time without a non-destructive detector to the average entanglement generation time with a non-destructive detector, \({T}_{{{\rm{ent}}}/{T }_{ {\rm{ent}}}^{{\rm{NPQD}}}\), the relationship with the channel length L. Choose the position of the detector so that \({T}_{{\rm{ent}} }^{{\rm{NPQD}}}\) is the smallest. Our non-destructive detector (solid line) is superior to direct transmission at channel distances greater than or equal to 14 kilometers, while a perfect NPQD (dashed line) has advantages at any distance. The second example (Figure 4b) describes a situation in which only if the qubit survives the transmission through the lossy channel, can it perform complex operations on the input photon qubit more efficiently . This can be achieved by placing an NPQD before operating the node. An example of complex operations is the quantum teleportation of photon qubits through the previously established long-distance entanglement. A good quality factor is the ratio of the probability P(1oq|0a) of a photon with a reflected qubit and the probability of a photon with an incoming qubit Piq after a non-destructive test, usually called qubit amplification24. For Piq ≪ 1, the qubit amplification is significantly higher than 1, and it will be significantly improved without the NPQD dark count (dashed line).

a, Entanglement generation between atom-photon entanglement source and harbinger quantum memory (HQM). Compared with the standard case, NPQD along the transmission channel can speed up the average sender-receiver entanglement time. The blue and green lines represent entanglement acceleration and NPQD entanglement time, respectively. b. The photon qubits are sent remotely to the receiver for subsequent operations involving precious resources (for example, long-distance entanglement). Qubit amplification gives the ratio of the probability of having a photon after the non-destructive test at the NPQD to the probability of having a photon before the test (Piq). c. The photon qubit is transferred to the noisy qubit measurement device (QMS). Using the NPQD pioneer signal to gate QMS can improve SNR. d, Pre-certified Bell test based on the presence of photons6. The dotted line in the figure represents the case of perfect NPQD (a, c) or NPQD (b) without dark numbers.

Another set of applications involves NPQD that can improve subsequent photon qubit measurements. Figure 4c shows a scenario in which photon qubits are sent to a remote receiver, which uses a noise detector for qubit measurements. The NPQD before the receiver only enables measurement when the qubit is not lost, thereby reducing the impact of measurement noise. This is particularly interesting for quantum key distribution, because the dark counting noise of classic detectors is an important limitation of quantum key rates for large distribution distances14. The signal-to-noise ratio (SNR) gain is defined as the ratio of SNR with NPQD to SNR without NPQD, namely SNRNPQD/SNR, and exceeds 1 when the transmitter-receiver distance L> 1 km. For longer distances, this ratio will converge to about 7, which can be improved by a lower NPQD dark count (represented by the dotted line considering the perfect NPQD parameter). The last example involves the non-vulnerability Bell test (Figure 4d). As mentioned previously6, the pioneer signal of NPQD allows two parties to determine that they share an entangled photon pair before the measurement, thereby helping to close the detection loophole. The important parameter here is the photon qubit reflection probability conditioned on its non-destructive detection. From our experiments, we found that \({\bar{n}}_{{\rm{oq}}}({0}_{{\rm{a}}})=0.56\pm 0.02\) for input | α|2 = 0.2 (Figure 3b). This value exceeds the minimum detection efficiency of 43% required for the asymmetric Bell test without detection loopholes (assuming there is no detector background noise).

In summary, we have demonstrated a non-destructive detector for photon polarization qubits. We expect that it should also apply to time bin qubits. The main feature is that the conditional detection efficiency is as high as (79±3)%, and the qubit preservation fidelity is at least (96.2±0.3)%. None of the observed limitations seem to be fundamental. Most importantly, we have proposed four possible applications that will benefit from our current devices, and we still hope to improve them. This leads us to believe that our detector will be a useful tool in the near-term quantum communication link and fundamental testing of quantum physics.

At the beginning of the experiment, a single atom was loaded into the two-second-long loading phase at the intersection of the two fiber cavity modes (details in Reference 26). The magneto-optical trap with 87Rb atoms is loaded about 10 mm above the fiber and released, so that the atoms cooled by the laser fall to the cavity area. At the intersection of the two cavity modes, there is a three-dimensional optical lattice in which a single atom is trapped. The lattice is composed of two blue detuned intracavity traps (774.6 nm and 776.5 nm wavelength) and a red detuned standing wave optical dipole trap (799.2 nm wavelength), detuned relative to the D line, and the trap depth is U0 / kB ≈ 1 mK (kB, Boltzmann's constant). The cooling beam enters and cools the individual atoms in the trap at an oblique angle, and stays there for a few seconds. The cooling light scattered by the atoms into the state detection cavity mode is then detected by the single-photon detector to confirm the existence of a single atom. After that, the NPQD scheme runs at a repetition rate of 576 Hz. The sequence is divided into three parts: atomic cooling, atomic state preparation and NPQD part. The length of the atomic cooling time accounts for 97% of the fast sequence time. This high ratio is accompanied by the required small microwave duty cycle to minimize system heating and cavity vibration caused by the applied microwave field. However, during such a long cooling time, we performed six 3-microsecond-long sequences to generate single photons emitted by atoms. The recorded photon count is used to calculate the autocorrelation function g(2)(0) = 1 − 1/n to infer the number of captured atoms n. After the atoms are cooled, there is a 30 μs-long optical pumping stage to prepare the atoms in the Zeeman state |F = 1, mF = 0⟩. Here, the applied laser field is the same as described in the reference. 26, except that we do not apply the final 4 microsecond long π-polarized laser field used in this work. After optical pumping, the sequence starts with the NPQD scheme reported in the main text. We have already said that for cavity-assisted state detection, the state detection cavity is close to resonance with the atomic transition D2: |F = 2⟩ ↔ |F' = 3⟩. Since the state detection cavity exhibits an intentional polarization mode split by more than four cavity linewidths, only the π polarization mode is close to resonance with the atomic transition; the second polarization mode is blue detuned.

The nondestructive detector scheme requires coherent operations on the atomic ground states |F = 1, mF = 0⟩ and |F = 2, mF = 0⟩. In our experiment, this operation is done by microwave radiation. In contrast to the Raman transition with a near-infrared radiation field, the use of a microwave field is advantageous, because the latter is essentially less detuned to the excited state, so it is more likely to fill these, which can lead to a decoherence process 34 .

The microwave antenna is placed in the vacuum chamber, less than 2 cm from the intersection of the fiber cavity mode. The antenna consists of a single ring with a circumference of 4.4 cm, which is equal to the wavelength of the microwave field. The permeance field of the order of 226.5 mG​​ defines the quantization axis along the cavity axis of the qubit, which allows us to resolve a single ground state transition with a microwave pulse duration of 5.8 μs. The expanded data Figure 1a shows the microwave spectrum of an atom prepared in the state |F = 1, mF = 0⟩, and then the atom is driven with a microwave field of different frequencies and a rectangular pulse duration of 25 μs. The final cavity assisted state detection measures the population in state 52S1/2 F = 2.

Choosing the relevant frequency can drive the transition of interest: |F = 1, mF = 0⟩ ↔ |F = 2, mF = 0⟩. The coherent Rabi flip of these two states is shown in the extended data Figure 1b, revealing a π/2 pulse duration of 5.8 μs. One limitation that affects this coherent drive is decoherence, which will reduce the visibility of Rabi oscillations. To further characterize this effect, we conducted a Ramsey type experiment (extended data Figure 1c). We applied two rectangular π/2 pulses with different time intervals between them. During the waiting time, the internal microwave clock is offset by 100 kHz to distinguish between decoherence and small microwave detuning. The decoherence is then clearly detected by the reduced visibility of the oscillations. The extended data Figure 1c shows how the visibility decreases to a value of 1/e (e, Euler number) after 121 μs, which we define as the coherence time. We suspect that decoherence is caused by the effect of mechanically non-ground-state cooling atoms, which are trapped by near-resonant red detuned optical dipole traps. Therefore, the hyperfine ground state |F = 1⟩ and |F = 2⟩ are different AC Stark shifts, which leads to different trap frequencies and eventually non-degenerate ground state transition frequencies. This situation can be improved by a single atom's ground state cooling or a further red detuned (and therefore more powerful) optical dipole trap.

One of the contributing factors of NPQD is the polarization-independent strong coupling between the atom and the photon qubit mediated by the qubit cavity. For characterization and measurement of reflectance spectra (extended data in Figure 2a), the detection field is in the left and right circular polarization superimposition, once an atom is coupled to the cavity mode (blue dot), and there is no atom (green dot) at one time. In the figure, the detection field is zero The frequency corresponds to the atomic transition frequency. The cavity spectrum produces a field decay rate of κQC = 2π × (34.6 ± 0.3) MHz when the qubit cavity length is 162 μm. The normal mode spectrum provides a coupling rate of g = 2π × (18.6 ± 0.5) MHz, which results in a synergy of-considering the atomic dipole attenuation rate of γ = 2π × 3 MHz-C = g2/(2κQCγ) = 1.67性±0.09. Note that the intensity reflection coefficient is the same as \(({R}_{|{0}_{{\rm{a}}}\rangle }=0.50\pm 0.02)\) and without \(({R} _{|{ 1}_{{\rm{a}}}\rangle }=0.117\pm 0.003)\) A coupling atom, both of which are close to zero detuning. The intensity reflection coefficient at the zero atom and cavity detuning can be calculated according to \(R={|1-{\mu }_{{\rm{fc}}}^{2}\tfrac{2{\kappa }_ {{ \rm{QC}},1}}{{\kappa }_{{\rm{QC}}}}\tfrac{1}{2C 1}|}^{2}\), it uses external coupling Mirror cavity field attenuation rate\({\kappa }_{{\rm{QC}},1}={\kappa }_{{\rm{QC}}}\times \tfrac{340\,{ \rm {ppm}}}{430\,{\rm{ppm}}\). The intensity reflection coefficient equation also considers the mode matching between the fiber and the cavity mode, μfc = 0.92e–i0.03, relative to the reference Equations provided in the literature. 9. The difference between the coefficients constitutes the main source of error of our non-destructive detector, resulting in a low detection probability, as described below.

The theoretical model given in the supplementary information includes a detailed set of contribution defects of our NPQD. However, here we assume that a perfect system detects single photons, and only conditioned reflection is a defect to clarify its impact on the detector. The NPQD scheme starts with atoms prepared in the superposition of two ground states\(|{\varPsi }_{{\rm{a}}1}\rangle =(|{0}_{{\rm{a}}} \rangle |{1}_{{\rm{a}}}\rangle )/\sqrt{2}\) ideally becomes \(|{\varPsi }_{{\rm{a}}2} \rangle =(|{0}_{{\rm{a}}}\rangle -|{1}_{{\rm{a}}}\rangle )/\sqrt{2}\) After the photon is successfully reflected (The blue and first red vectors in Figure 2b of the extended data). However, due to the different cavity reflection coefficients corresponding to the two atomic states, the initial state becomes

Use \({r}_{0}=|\sqrt{{R}_{|{0}_{{\rm{a}}}\rangle }}|\) and \({r}_{1 }=|\sqrt{{R}_{|{1}_{{\rm{a}}}\rangle }}|{{\rm{e}}}^{{\rm{i}}{\ rm{\pi }}}\) (the first green vector). Because r0 and r1 are not only different in phase but also different in size, the atomic state has left the equatorial plane of the Bloch sphere. The subsequent microwave π/2 pulse rotates this state to \(|{\varPsi }_{{\rm{a}}3}\rangle ={\hat{R}}_{a}({\rm{\ pi }}/2)|{\varPsi }_{{\rm{a}}2}\rangle \) exceeds the pole |0a⟩ (the second green vector), thus resulting in a state 1a⟩ that is not orthogonal to | Then, the upper limit of the detection probability of qubit reflection is P(0a|1oq) = |⟨ 0a|Ψa3⟩ |2 = 89%. The further decrease in this value we observed is due to a set of defects discussed further in the supplementary information.

As shown in Figure 2, the photon polarization qubit undergoes a small rotation after its non-destructive testing. This is due to the birefringence of the qubit cavity, which originates from the small ellipticity of the fiber cavity mirror and causes polarization mode splitting by one-fifth of the line width of the 36 qubit cavity. Through the λ/2 retardation plate located behind the cavity, all polarization states are rotated, so that the eigenmode polarization of the qubit cavity during reflection is rotated to polarizations A and D during the detection setting. We measured that in the case of a cavity, the superposition of polarizations A and D is rotated 42° around the A/D axis on the Bloch sphere. The detector scheme relies on atoms in a superposition of coupled and uncoupled states, so the incoming photon qubits will not undergo this complete rotation. The 19.6° rotation angle was extracted from the fit of the input and output polarization states, which were measured by polarization state tomography (extended data Figure 3a; analysis follows the description in Reference 26). This rotation is also observed in the extended data Figure 3b, which shows the matrix of the relevant fundamental quantum processes of the detector. The displayed matrix is ​​derived from the maximum likelihood fitting, and the uncertainty of the matrix elements is calculated based on the reference. 26. The main contributing matrix elements are χ0,0, χ1,0 and χ0,1, which illustrate the polarization rotation effect.

In this article, we provide the average state fidelity under non-destructive testing conditions. However, evaluation of unconditional SPD counts (for example, events from all photon qubits reflected by NPQD) shows that the polarization state fidelity of the extrinsic polarization of the cavity is reduced (compare \( {\mathcal F} \) conditions and \( {\mathcal F} \) uncond. In the extended data table 1). We attribute this to the partial entanglement effect between the polarization state of the photon and the atomic state, because the polarization rotation preferably occurs when the atom is in the uncoupled state. This effect can theoretically be described as follows. The initial atomic superposition state and the incident photon qubit cause a partial entangled state after reflection,

|0a⟩ and |1a⟩ represent the coupled and uncoupled atomic states, respectively, |Ψph⟩ represents the photon polarization state, when the atom is in the state |1a, it undergoes rotation \(\hat{R}\)⟩. R0 and r1 The field reflection coefficient used in the method section "Atom-cavity interaction and conditioned reflection" is described. In addition, we assume that there is no qubit rotation in the case of coupled atoms. When the atomic part is not observed, the entanglement is transformed into the decoherence of the photon qubits, as shown by the reduced sphere in the expanded data Figure 3c. This situation only applies to polarization states that are rotated due to cavity birefringence. Because the photon polarizations A and D do not rotate, for these polarizations, the state in equation (2) becomes separable, thus following the ideal situation.

As mentioned earlier, polarization rotation can cause qubits to be fidelity, which can be overcome by retarding wave plates. However, in addition, people also expect the polarization dependence of the phase shift of the imprinted atoms when the qubit is reflected, which will affect the efficiency of non-destructive testing. We tried to observe this effect by comparing the performance of detectors with different incident polarization states (Figure 3), but no substantial difference in NPQD performance was found. We attribute this observation to the fact that the birefringence effect is relatively small compared to other defects (such as conditioned reflection).

In Figure 4, we show a simulation of a specific situation where our non-destructive detector is advantageous. This section will explain the details of these simulations. Since the working wavelength of our NPQD is 780 nm, we consider the photon qubit of this wavelength, and the corresponding fiber attenuation is αatt = 4 dB km-1.

Case 1 (Figure 4a) describes the long-distance entanglement between the atom-photon entanglement source and the predictive quantum memory. For simplicity, we consider the ideal case where the time required to entangle the two systems is given by the communication time (for example, the time to distribute entangled photon qubits plus the time to return to communication if the omen is stored successfully). In this case, the average entanglement time is given by Tent = 2L/(cpent), where L is the distance between the transmitter and receiver, c is the speed of light in the fiber, and pent = ηAP\({10}^{ -{\alpha }_{{\rm{a}}{\rm{t}}{\rm{t}}}L/10}\) ηH is the probability of entanglement distribution. This probability depends on the atom-photon entanglement source efficiency ηAP, the attenuation coefficient α of the transmission channel, and the prediction efficiency ηH of the predictive quantum memory.

When NPQD is inserted along the transmission channel at a distance l <L from the sender, the average entanglement time is \({T}_{{\rm{ent}}}^{{\rm{NPQD}}}= 2\langle l\rangle /(c{p}_{{\rm{ent}}}^{{\rm{NPQD}}})\). Compared with Tent, the average communication distance ⟨l⟩ replaced L, by ⟨l⟩ = P(0a)L [1 − P(0a)](l tNPQDc/2) is given. It has two terms: First, NPQD can provide non-destructive testing events together with the full distance L. Secondly, NPQD does not detect any qubit photons, resulting in the effective distance being shortened to 1. In this case, the NPQD pioneer signal readout time tNPQD must be considered, which will delay subsequent classical communications. Both terms include the probability of a non-destructive detection event, namely

  It considers the nondestructive detection probability of incoming qubit P(0a|1iq) and NPQD dark count pDC. In addition to replacing L with ⟨l⟩ in \({T}_{{\rm{ent}}}^{{\rm{NPQD}}}\), it is also necessary to provide the existence of the entanglement probability NPQD \ ({p}_{{\rm{ent}}}^{{\rm{NPQD}}}\), it replaced pent. It is composed of \({p}_{{\rm{ent}}}^{{\rm{NPQD}}}={p}_{{\rm{ent}}}P({0}_{ {\ rm{a}}}|{1}_{{\rm{iq}}})P({1}_{{\rm{oq}}}|{0}_{{\rm{a} }} )\) The low efficiency of NPQD is also considered. With these expressions at hand, we calculate the entanglement time \({T}_{{\rm{ent}}}^{{\rm{NPQD}}}\) and compare it with the case where the non-destructive detector is not included Tent to get entangled to accelerate. For these two simulations, we consider ηAP = 0.5 and ηH = 0.11, which are the realistic parameters obtained in previous work 26,38.

Case 2 (Figure 4b) describes the amplification of qubits with different probabilities of the number of input photons. The qubit amplification rate Aq is defined as the ratio of the probability of having a photon qubit at the output of the NPQD and its nondestructive detection P(1oq|0a) to the probability of having an input qubit Piq. These quantities are related to the quantities shown in Figure 3, from which it is inferred that the qubit magnification is \({A}_{{\rm{q}}}={\bar{n}}_{{\rm{oq} }}({0}_{{\rm{a}}})/|\alpha {|}^{2}\) is used for small|α|2. The data points shown in Figure 4b are calculated based on this expression. In order to simulate qubit amplification using our NPQD parameters (solid line) and no NPQD dark count (dashed line), we use the theoretical model described in the supplementary information.

In case 3 (Figure 4c), the remote photon qubit is measured with a noise detector: NPQD gated qubit measurement to improve its signal-to-noise ratio, SNR = ps/pn. This gating reduces the probability of noise detection to \({p}_{{\rm{n}}}^{{\rm{NPQD}}}}=P({0}_{{\rm{a}} }) {p}_{{\rm{n}}}\) But due to the parasitic loss caused by the non-destructive tester, \({p}_{{\rm{s}}}^{{ \rm{NPQD} }}={p}_{{\rm{s}}}P({0}_{{\rm{a}}}|{1}_{{\rm{iq}}} )P({1 }_{{\rm{oq}}}|{0}_{{\rm{a}}})\). In addition, we compare the probability of non-destructive testing with our NPQD parameter P(0a) = P(0a| 1iq)ps(1 – pDC) pDC is correlated, and considering that the input signal probability depends only on the transmission loss of the communication channel, ps = \({10}^{-{\alpha }_{{\rm{a}}{ \rm{t}}{\rm{t}}}L/10}\). This allows us to calculate the SNR gain as a function of the communication distance L, considering the NPQD (solid line) with our parameters and the perfect NPQD (dashed line).

The data set generated and/or analyzed during the current study is available at https://doi.org/10.5281/zenodo.4381767.

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We thank M. Brekenfeld and JD Christesen for their contributions in the early stages of this work. This work was supported by the Bundesministerium für Bildung und Forschung through Verbund Q.Link.X (authorization number 16KIS0870), Deutsche Forschungsgemeinschaft under the German Excellence Strategy (EXC-2111, 390814868) and the European Union Research Horizon 2020 Innovation Project Internet Alliance (GA No. 820445). PF recognizes the support of the Cellex-ICFO-MPQ Postdoctoral Fellowship Program.

Open access funding provided by the Max Planck Society.

Max-Planck-Institut für Quantenoptik, Garching, Germany

Dominic Nimitz, Paul Farrera, Stefan Langenfeld and Gerhard Lemper

ICFO—Institut de Ciencies Fotoniques, Barcelona Institute of Science and Technology, Castelldefels, Spain

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a, the microwave spectrum of the atom prepared in the Zeeman state |F = 1, mF = 0⟩. The light blue curve is a fit composed of three sinc2 functions. The fitting parameters are the center and Rabi frequency of each conversion, and the pulse duration is fixed at 25 μs. The peak at 0 kHz corresponds to the |0a⟩ ↔ |1a⟩ transition. b. The microwave-driven Rabi oscillation is used on the |0a⟩ ↔ |1a⟩ transition for atoms prepared in the state |0a⟩. c. The atoms prepared in the state of |0a⟩ are then driven by a microwave π/2 pulse into the superposition of |0a⟩ and |1a⟩. After the variable time, a second microwave π/2 pulse is applied. During the waiting period, the internal microwave clock is offset by 100 kHz. The final state measures the population in |1a⟩. All error bars represent the 1σ confidence interval, and some error bars are smaller than the symbol size.

a, The cavity reflection spectrum of a qubit cavity without atoms (green dots), and the cavity mode is strongly coupled with the atoms prepared in the state |F = 1, mF = 0⟩ (blue dots). The solid line represents the fitting function, and the error bar represents the standard deviation. b. Bloch spheres have atomic states (represented by vectors) at different stages of the detector scheme. The blue vector is the initial atomic state after the first π/2 microwave pulse. After the photon is reflected, the initial state changes to a red or green state (the dotted arrow is a guide for the eyes). The green and red states show the condition of conditioned reflex and unconditional reflex, respectively. The subsequent microwave π/2 pulse rotates the atom to its final state (the dashed arrow follows the rotation). State detection (not shown) then projects the atomic state onto |0a⟩ or |1a⟩.

a, c, Poincaré sphere shows the basic quantum process of our NPQD. The colored sphere is the result of polarization tomography of reflected photon pulses corresponding to the colored and labeled input polarization. b, d, NPQD basic quantum process matrix χ, reconstructed by maximum likelihood fitting. \({{\mathbb{1}}}_{2}\) represents a 2 × 2 identity matrix, and σx, σy and σz represent Pauli matrices. In a and b, the photon count of the tomography setting depends on the non-destructive qubit detection. In c and d, they are not conditional on non-destructive testing. The rotation around the A/D axis is described by an operator constructed by σx. The uncertainty of χm,n is evaluated by the Monte Carlo method and represents the standard error.

This file contains supplementary text on theoretical models of NPQD and photon Fock state qubit distillation.

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Niemietz, D., Farrera, P., Langenfeld, S. etc. Non-destructive testing of photon qubits. Nature 591, 570–574 (2021). https://doi.org/10.1038/s41586-021-03290-z

DOI: https://doi.org/10.1038/s41586-021-03290-z

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