Coherent and reversible mapping of quantum information between light and matter is an important experimental challenge in quantum information science. In particular, it is an essential requirement for the implementation of quantum networks and quantum repeaters1,2,3. So far, quantum interfaces between light and atoms have been demonstrated with atomic gases4,5,6,7,8,9, and with single trapped atoms in cavities10. Here we demonstrate the coherent and reversible mapping of a light field with less than one photon per pulse onto an ensemble of ∼107 atoms naturally trapped in a solid. This is achieved by coherently absorbing the light field in a suitably prepared solid-state atomic medium11. The state of the light is mapped onto collective atomic excitations at an optical transition and stored for a pre-determined time of up to 1 μs before being released in a well-defined spatio-temporal mode as a result of a collective interference. The coherence of the process is verified by performing an interference experiment with two stored weak pulses with a variable phase relation. Visibilities of more than 95 per cent are obtained, demonstrating the high coherence of the mapping process at the single-photon level. In addition, we show experimentally that our interface makes it possible to store and retrieve light fields in multiple temporal modes. Our results open the way to multimode solid-state quantum memories as a promising alternative to atomic gases.
Efficient and reversible mapping of quantum states between light and matter requires strong atom–photon interaction. This can be achieved using ensembles of atoms, where light can be efficiently absorbed and where it is possible to engineer the atomic systems such that the stored light can be retrieved in a well-defined spatio-temporal mode owing to there being a collective constructive interference between all the emitters. This collective enhancement is at the heart of protocols for storing photonic quantum states in atomic ensembles, such as schemes based on electromagnetically induced transparency (EIT)12, off-resonant Raman interactions13 and modified photon echoes using controlled reversible inhomogeneous broadening (CRIB)14,15 and atomic frequency combs (AFC)11.
Certain solid-state systems have properties that make them very attractive for applications in quantum state storage. In particular, solids doped with rare-earth ions provide a unique physical system in which large ensembles of atoms are naturally trapped in a solid-state matrix, which prevents decoherence due to the motion of the atoms. These systems exhibit excellent coherence properties at low temperature (below 4 K), both for the optical16 and the spin transitions17. Classical light has been stored for more than 1 s in a rare-earth-doped solid18. The long optical coherence times enable storage of multiple temporal modes in a single quantum memory, which promises significant speed increases in quantum repeater applications3. Furthermore, the high optical densities required to achieve high-efficiency light storage and retrieval can be obtained. However, despite recent experimental progress18,19,20,21,22,23, the implementation of a solid-state light–matter quantum interface has not yet been reported.
Here we demonstrate the coherent mapping of light at the single-photon level onto a large number of atoms in a solid, and collective re-emission of the stored light at a pre-determined time. Time-delayed interferometry with weak X-ray pulses scattered by collective states of iron nuclei was demonstrated in this context in ref. 24. In our experiment in the optical regime, the mapping is done by coherently absorbing the light in an ensemble of inhomogeneously broadened atoms spectrally prepared with a periodic modulation of the absorption profile11,25. The reversible absorption by such a spectral grating is at the heart of the recently proposed multimode quantum memory scheme based on AFC11. We therefore also demonstrate a proof of principle of an essential primitive of this protocol at the single-photon level.
Let us now describe how our interface works. The inhomogeneous spectral atomic distribution at the optical transition between the ground state, |g〉, and the excited state, |e〉, is shaped into a series of absorbing peaks of width γ, with a peak separation Δ (Fig. 1a). This can be done using optical pumping techniques, as discussed later. Once the spectral grating is prepared, we send in weak coherent states of light, |α〉L, with mean photon number = |α|2 < 1. The bandwidth of each photon must be larger than Δ but smaller than the total width of the grating. It is then possible to show that the light can be absorbed uniformly over its entire frequency spectrum, although the atomic spectral distribution has large gaps11. This can be understood from the time–energy Heisenberg uncertainty relations. Over the short timescale given by the duration, τP, of the photon, the linewidth of the atomic resonance is effectively broadened to a value of order 1/τP > Δ, resulting in a uniform, but smaller, absorption. The effective optical depth of the spectral grating is given by ≈ d/F, where F = Δ/γ is the finesse of the spectral grating and d the grating optical depth.
After absorption, the light field is stored in a coherent superposition of collective optical excitations delocalized over all the resonant atoms in the grating. The state of the atoms (not normalized) can be written aswhere |0〉A = |g1gN〉 andHere N is the total number of atoms; |gj〉 and |ej〉 represent the ground and excited states, respectively, of atom j; zj is the position of atom j; k is the wavenumber of the light field (for simplicity, we only consider the forward-propagating spatial mode); δj is the detuning of the atom with respect to the laser frequency; and the amplitudes cj depend on the frequency and on the spatial position of atom j. This collective state will rapidly dephase because each term acquires an individual phase . For narrow absorption peaks, the detunings can be written δj = mjΔ, where mj are integers. Owing to this periodic structure of the absorption profile, the collective state will then be re-established after a pre-determined time 2π/Δ. This leads to a coherent photon-echo-type re-emission in the forward spatial mode11,25. If the absorption peaks have a finite width, the rephasing will not be perfect, leading to a reduction of the collective signal11, as discussed below and in the Supplementary Information. We note that in our experiment the light field is stored as a collective excitation at the optical transition, contrary to all previous light storage experiments at the single-photon level, where collective excitations of spin states were used5,6,7.
The solid-state interface is implemented in an ensemble of neodymium ions (Nd3+) doped into a YVO4 crystal26. The Nd3+ ions constitute an ensemble of inhomogeneously broadened atoms having a relevant level structure with two spin ground states, |g〉 and |aux〉, and one excited state, |e〉, as shown in Fig. 1. Initially, the two ground states are equally populated for all frequencies within the inhomogeneous broadening. The preparation of the spectral grating is achieved by frequency-selective optical pumping from |g〉 to |aux〉 through the excited state |e〉 (see Fig. 1 for an overview of the experiment). This is implemented with a Ramsey-type interference using a train of coherent pairs of pulses27 (Fig. 1, Methods). To store weak light fields, it is required that there be no population in the excited state, as otherwise fluorescence will blur the signal. This is ensured by waiting long enough between the preparation and storage sequences for all atoms to return to the ground states. As a result of the preparation sequence, a spectral grating is present in |g〉 before the storage begins. The grating decays with the population relaxation lifetime TZ between the spin states (TZ = 6 ms in our case).
In the first experiment, we demonstrate collective mapping of weak coherent states of light, |α〉L, onto the crystal. An example with = 0.5 is shown in Fig. 2 (See Methods for the estimation of ). When the sample is prepared with a spectral grating having a periodicity of 4 MHz, we observe a strong emission at the expected storage time of 250 ns. The measured storage and retrieval efficiency is η ≈ 0.005, which means that 0.5% of the incoming light is re-emitted in this signal. Although η is low, the re-emission probability is more than four orders of magnitude larger than what would be expected from a non-collective spontaneous re-emission, taking into account that we collect a solid angle of 2 × 10-4 and that the optical relaxation time is three orders of magnitude greater than the observed signal time. This signal thus clearly arises from a collective re-emission, which demonstrates the collective and reversible mapping of a light field with less than one photon on average onto a large number of atoms in a solid. To further study the mapping process, we record the number of counts in the observed signal for values of ranging from 0.2 to 2.7 (Fig. 3a). This shows that the mapping is linear and that very low photon numbers can still be mapped and retrieved. We also investigated the decay of storage efficiency with storage time (Fig. 3b).
So far we have considered the storage of weak light fields in a single temporal mode. However, the use of spectral gratings also allows for storage in multiple temporal modes, as pointed out in ref. 11. To illustrate this multimode property, we store trains of four weak pulses, with values of ranging from 0.8 to 0.3, for 500 ns, as shown in Fig. 4. The maximal number of modes that can be stored is given by the ratio of the storage time (determined by the spectral grating) to the duration of an individual mode. In the present experiment, the shortest duration of pulses was set to about 20 ns (full-width at half-maximum) by technical limitations. A great advantage of the AFC protocol is that the number of modes that can be stored does not depend on the optical depth, unlike for EIT and CRIB11.
For applications in quantum memories, it is crucial that the interface conserves the phase of the incoming pulses. To probe the coherence of the mapping process, we store a pair of weak pulses that are separate by a time τ = 100 ns and have a variable relative phase, Φ. This can be viewed as a time-bin qubit, which can be written as |ψ〉L = |αt〉L + eiΦ|αt+τ〉L, where |αt〉L represents a weak coherent state of light at time t. The qubit is stored and thereafter analysed directly in the memory21. This method requires the implementation of partial readouts at different times. This realizes a projection on a superposition basis, similar to what can be done with an unbalanced Mach–Zehnder interferometer21. If the time, τ, between the weak pulses matches the time between the two readouts, the re-emission from the sample can be suppressed or enhanced depending on the phase, Φ. The visibility of this interference is a measure of the coherence of the mapping process. The two partial readouts are made by preparing two superimposed spectral gratings of different periods, corresponding to respective storage times of 200 and 300 ns. An example of interference for = 0.85 is shown in Fig. 5. We measured net visibilities (that is, after subtraction of detector dark counts) above 95% for various values of between 0.4 and 1.7, which demonstrates the high coherence of the storage process, even at the single-photon level. This excellent phase preservation results from the collective enhancement22 and the almost complete suppression of background noise.
We now analyse in more detail the efficiency performance of our interface using the model developed for the AFC quantum memory11. The efficiency of the storage and retrieval in the forward mode, for an ideal AFC, is given by (Supplementary Information)The first factor represents the collective interaction, which is proportional to the square of the number of atoms in the spectral grating. The second factor describes the intrinsic AFC dephasing during the storage due to the finite width of the absorption peaks. The last factor accounts for the re-absorption of the emitted photon by the resonant atoms. In the present experiment, imperfect optical pumping results in a uniform absorbing background with residual optical depth d0 that will act as a passive loss. The efficiency is then given by η = ηAFC (Supplementary Information). Using the model presented in the Supplementary Information, we estimate that F ≈ 2, d = 1.44 ± 0.08 and d0 = 2.28 ± 0.14. This large value of d0 means that 90% of incoming photons are lost to the background atoms, which do not give rise to a collective emission.
To analyse the physics of the collective enhancement further, it is informative to infer the intrinsic storage efficiency, ηAFC, that could be obtained in the absence of an absorbing background. Using equation (1) and the values of d and F, we find that ηAFC = 0.04. The intrinsic storage efficiency can be further decomposed into two terms, the write efficiency (ηw) and the read efficiency (ηr), such that ηAFC = ηwηr. The write efficiency is defined as the probability that a photon is coherently absorbed by the atoms of the AFC: ηw = 1 - e-d/F = 0.51. This implies that the read efficiency, that is, the probability that the photon is re-emitted in the collective mode conditioned on a coherent absorption, is ηr = 0.085. To increase the write efficiency, we must increase the optical depth. The read efficiency is mostly limited by the intrinsic dephasing during the storage, owing to the low finesse, F ≈ 2. In our experiment, F is limited by the minimal width of the absorption peak, which is of order 1–2 MHz owing to the linewidth of our free-running laser and to material properties (Fig. 3).
We emphasize, however, that these are not fundamental limitations of rare-earth-doped materials. The preparation of narrow absorption lines with a low absorption background has been demonstrated for several other rare-earth-doped materials, such as Eu3+:Y2SiO5 (ref. 19), Pr3+:Y2SiO5 (refs 20,28) and Tm3+:YAG (ref. 29). Significantly higher storage efficiencies should be obtained in these materials. Ultimately, the efficiency of the forward retrieval is limited to 54%, owing to the re-absorption of the collective signal11. This can be overcome by using backward retrieval; see below.
To use our interface in a quantum repeater architecture, several further steps must be undertaken. The photon to be stored must be correlated with another photon that will be sent over long distances3. Moreover, on-demand readout of the stored field and longer storage times are required. This is possible by transferring the excitations in |e〉 to another long-lived, ground-state spin level, |s〉, using an optical control pulse11, as for other quantum memory proposals, such as EIT or Raman-based schemes30. For on-demand readout, the excitation can be transferred back to |e〉 using another control pulse at a chosen time. Efficient and coherent transfer in an optical Λ configuration has been demonstrated in praseodymium-doped solids28, which possess the necessary level structure of three ground-state levels (|g〉, |aux〉 and |s〉). For neodymium, hyperfine states may also in principle be used. The pair of optical control pulses, if applied in a counter-propagating fashion, also change the phase pattern of the stored excitation, such that the collective field will be re-emitted backward. Then the storage efficiency can approach unity, owing to a constructive interference that effectively suppresses re-absorption11
We have demonstrated the collective and reversible mapping of a light field with less than one photon on average onto a large number of atoms embedded in a solid. This represents the observation of collective enhancement at the single-photon level in a solid in the optical regime. We have also demonstrated that the quantum coherence of incident weak light fields is almost perfectly conserved during the storage. Solid-state systems can therefore be considered as a promising alternative to atomic gases for photonic quantum storage. This line of research holds promise for the implementation of efficient, long-distance quantum networks.
The spectral grating is prepared using a series of pulse pairs of pulse area θ < π/2 resonant with the |g〉 → |e〉 transition. Each pair of pulses produces a frequency-selective coherent transfer of population from |g〉 to |e〉27. This can be seen as a Ramsey-type interference in which the two light pulses act as beam splitters and the phase shift acquired in the excited state depends on the detuning of the atoms. The periodicity of the created spectral grating is then given by the inverse of the time interval, τs, between the two pulses. The atoms in the excited state can decay to both ground states, |g〉 and |aux〉, with a relaxation time of T1 = 100 μs. The atoms that decay to |aux〉 are not affected by the preparation laser and remain in this state for a time TZ = 6 ms (ref. 26). The pulse sequence is then repeated 100 times with a time separation between the pairs of 15 μs, which is longer than the optical coherence time, T2 = 7 μs. This allows for the build-up of the spectral grating, with population storage in |aux〉. For the interference experiment, the two gratings corresponding to storage times of 200 and 300 ns are created in a similar way. Each grating is prepared with a pulse pair having the corresponding time separation, sent alternately with a time separation of 7.5 μs.
To estimate the mean number of photons per pulse, we shift the laser out of resonance with the absorbing atoms and record the proportion of detections in the single-photon counter (typically between 1% and 20%). By a careful measurement both of the detection efficiency (ηd = 0.32) and of the transmission efficiency from the input face of the cryostat to the detector (typically ηt = 0.2), we can infer the mean number of photons in front of the cryostat, before the sample.
We thank E. Cavalli and M. Bettinelli for kindly lending us the Nd:YVO4 crystal. This work was supported by the Swiss NCCR Quantum Photonics and by the European Commission under the Integrated Project Qubit Applications.
This file contains Supplementary Data including Supplementary Figures 1-3 with Legends and a Supplementary Reference
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Scientific Reports (2018)