A quantum memory is a stationary system or device, which can maintain a quantum state for a desired amount of time after which the state must be able to be read out either in the form or a non-stationary quantum system or via a classical projection measurement. In that sense, quantum memory is relevant for networks if the quantum state can be mapped either from or to (ideally both) a non-stationary system carrying the quantum state, which in essence means an optical photon. When gauging the quality of quantum memory, according to e.g. its storage efficiency, time, fidelity, bandwidth and multimode capacity, it is important to optimize according to the properties that matter for the particular application. As an example, for quantum memory used to buffer qubits in an optical quantum processor the storage time may be less of a concern than the bandwidth. The research in the QCloudLab focuses on developing efficient quantum memory for quantum repeaters.
Optical quantum memory has been implemented in diverse physical systems such as warm-gasses [BJ04], single-trapped atoms [HPS11], diamond colour centres [AR16], and rare-earth ion (REI) doped materials [JJL05, BK06, MA09], to name a few. REI materials have many desirable properties for quantum memory. They can feature very long coherence times – up to several ms on optical transitions and several hours on spin transitions – which allows optical storage that may be transferred to spin transitions. The collective enhancement leads to large photon absorption probabilities, which yield fast optical interaction. The inhomogeneous broadening translates into large memory bandwidths and multimode storage capacity. The existence of long-lived shelving levels allows for spectral tailoring as is needed in many photon-echo type quantum memories.
In the QCloudLab we focus on the Atomic Frequency Comb protocol [MA09] due to its important and unique multi-mode storage capacity and large bandwidth. Past work at the UofC resulted in the first demonstration of entangled photon-storage in a solid-state material using a waveguide defined in a thulium doped lithium-niobate (Tm:LiNbO3) crystal. This was followed by a demonstration of storage of entangled telecom-wavelength photons in a erbium doped silica fibre (Er:SiO2) and finally simultaneous storage of both entangled photons of a pair – one in Tm:LiNbO3 and one in Er:SiO2. Other experiments have shown preservation of indistinguishability of stored photons, storage of polarization qubits encoded in heralded single photons at telecom wavelength, storage of telecom wavelength photons in erbium doped lithium niobite waveguides using super-hyperfine levels, and spectrally multimode storage in Tm:LiNbO3. These demonstrations of quantum memory are based on detailed spectroscopic studies of the materials, which is an ongoing research direction in the QCloudLab.
Current projects:
Past seminal experiment at the UofC employed Tm doped lithium-niobate, which excels in terms of large bandwidth and relatively large dipole interaction strength. However, material studies have revealed that due to a combination of undesirable branching ratios during optical pumping, spin inhomogeneous broadening and spectral diffusion it is difficult to achieve efficient quantum memory in this material. Furthermore, the excited state lifetime of about 100 ms sets an upper limit to the storage time, which is insufficient for long-distance quantum repeaters. As an alternative thulium doped yttrium-gallium garnet (Tm:YGG) has been found to have the sufficient coherence time and to be able to store heralded single photons [CWT14a, CWT14b, NS18]. Due to a combination of material imperfections and limited linewidth of the employed laser the storage time and the true capability of Tm:YGG has not yet been explored. Using new narrow linewidth lasers we are currently continuing our investigation of Tm:YGG. At the same time new boules of Tm:YGG will be grown with the aim of removing some of the material imperfections in earlier batches.
One trade-off with our quantum memory is the interaction strength of ensemble of rare-earth ions with light versus the coherence time of the transition. In general, a larger interaction strength, which will increase the probability of absorbing the incident photon, is associated with a shorter excited state lifetime, which also forms the upper bound to the coherence time. Indeed, the coherence time is often significantly shorter than the lifetime-limit, but there tends to be a relation between the orders of magnitude of both. The shorter coherence time will cause dephasing of the stored quantum state and thus reduce the efficiency of the memory. To compensate a low interaction strength, one may increase the size of the ensemble i.e. increase the doping concentration of the rare-earth ions. However, at some value the rare-earth concentration will start to perturb the host crystal to an extent that the coherence time is again affected negatively.
Fortunately, there is a way to overcome the low interaction strength – typically gauged by the material’s optical density – by incorporating the rare-earth ion doped crystal in an impedance matched cavity [MA10]. Indeed, this cavity enhanced AFC protocol is most efficient – approaching 100% – for low optical depths. The basic notion of the scheme is that interference between light directly reflected at the front of the cavity interferes destructively with the light that reaches the front surface after traversing the cavity and the memory material. Hence, the light to be stored is prevented from escaping the cavity until it is fully absorbed in the crystal. At the same time the recall occurs in a fashion where the transverse spatial mode adds up phase-coherently and ensures that none of the light is reabsorbed by the memory. These two effects combined allow for near unity efficiency. The impedance matched cavity AFC memory was first demonstrated in [MS13] (using Pr3+∶Y2SiO5, reaching 56% efficiency and about 2 MHz bandwidth) and subsequently in [PJ14] (using Eu3+:Y2SiO5, reaching 53% two-level AFC efficiency and about 1 MHz bandwidth) with the added feature of spin-wave storage with 12% overall efficiency.
In the QCloudLab we have implemented the cavity AFC memory in a thulium doped yttrium-aluminium-garnet (Tm:YAG). As in previous realizations, we directly coat the surfaces of the crystal and thus shape a simple planar-cavity. Compared to other cavity AFC demonstrations, the absence of hyperfine levels in the Tm ions, means that the Tm:YAG crystal has a larger potential bandwidth. In our current design we can reach up to 500 MHz bandwidth. Our most recent experiment has been to store time-bin qubits encoded in heralded single photons.
