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arXiv:1511.07787 · Europhysics Letters (EPL)

Multivariate quantum memory as controllable delayed multi-port beamsplitter

Anton N. Vetlugin, I. V. Sokolov

Published Mar 1, 2016• 11 citations

Abstract

The addressability of parallel spatially multimode quantum memory for light allows one to control independent collective spin waves within the same cold atomic ensemble. Generally speaking, there are transverse and longitudinal degrees of freedom of the memory that one can address by a proper choice of the pump (control) field spatial pattern. Here we concentrate on the mutual evolution and transformation of quantum states of the longitudinal modes of collective spin coherence in the cavity-based memory scheme. We assume that these modes are coherently controlled by the pump waves of the on-demand transverse profile, that is, by the superpositions of waves propagating in the directions close to orthogonal to the cavity axis. By the write-in, this allows one to couple a time sequence of the incoming quantized signals to a given set of superpositions of orthogonal spin waves. By the readout, one can retrieve quantum states of the collective spin waves that are controllable superpositions of the initial ones and are coupled on demand to the output signal sequence. In a general case, the memory is able to operate as a controllable delayed multi-port beamsplitter, capable of transformation of the delays, the durations and time shapes of signals in the sequence. We elaborate the theory of such light-matter interface for the spatially multivariate cavity-based off-resonant Raman-type quantum memory. Since, in order to speed up the manipulation of complex signals in multivariate memories, it might be of interest to store relatively short light pulses of a given time shape, we also address some issues of the cavity-based memory operation beyond the bad cavity limit.

DOI: 10.1209/0295-5075/113/64005

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The addressability of parallel spatially multimode quantum memory for light allows one to control independent collective spin waves within the same cold atomic ensemble. Generally speaking, there are transverse and longitudinal degrees of freedom of the memory that one can address by a proper choice of the pump (control) field spatial pattern. Here we concentrate on the mutual evolution and transformation of quantum states of the longitudinal modes of collective spin coherence in the cavity-based memory scheme. We assume that these modes are coherently controlled by the pump waves of the on-demand transverse profile, that is, by the superpositions of waves propagating in the directions close to orthogonal to the cavity axis. By the write-in, this allows one to couple a time sequence of the incoming quantized signals to a given set of superpositions of orthogonal spin waves. By the readout, one can retrieve quantum states of the collective spin waves that are controllable superpositions of the initial ones and are coupled on demand to the output signal sequence. In a general case, the memory is able to operate as a controllable delayed multi-port beamsplitter, capable of transformation of the delays, the durations and time shapes of signals in the sequence. We elaborate the theory of such light-matter interface for the spatially multivariate cavity-based off-resonant Raman-type quantum memory. Since, in order to speed up the manipulation of complex signals in multivariate memories, it might be of interest to store relatively short light pulses of a given time shape, we also address some issues of the cavity-based memory operation beyond the bad cavity limit.

We present a new scheme of quantum memory for optical images (spatially multimode light fields) that allows mapping the quantum state of the signal onto the long-lived coherence of the ground state of an ensemble of stationary atoms or impurity centers. The memory medium is embedded in an optical cavity with degenerate transverse modes, which increases the effective optical thickness of the medium and allows one, in principle, to store information in optically thin atomic layers. Since, in reality, storage and retrieval of limited-duration signals, including signals shorter than the lifetime of the field in the cavity, is of interest, we do not use the low- Q cavity approximation. The influence of losses due to partial reflection of the nonstationary signal field incident on a coupling mirror on the storage efficiency is considered. We used the method of approximate impedance matching, wherein losses due to reflection can be minimized by controlling the coupling parameter of the light field with memory medium in time, thus creating conditions for destructive interference of the signal and local fields on the coupling mirror. The influence of diffraction on the transverse resolution of memory at the writing and readout stages is investigated, and the number of effectively stored transverse spatial modes of the signal is estimated.

Abstract A device being a pinnacle of development of an optical quantum memory should combine the capabilities of storage, inter-communication, and processing of stored information. In particular, the ability to capture a train of optical pulses, interfere them in an arbitrary way and finally, perform on-demand release could realize arbitrary optical computation. Here we demonstrate the operation of a coherent optical memory being able to store optical pulses in the form of collective spin-wave excitations in a two-dimensional wavevector space. During storage, we perform complex beamsplitter operations and demonstrate a variety of protocols implemented at the processing stage, including real-time controlled interference of a pair of spin-wave modes with 95% visibility. The highly multimode structure of the presented memory lends itself to enhancing classical optical telecommunication, as well as parallel processing of optical qubits at the single-photon level.

A scheme for spatial multimode quantum memory is developed such that spatial-temporal structure of a weak signal pulse can be stored and recalled via cavity-assisted off-resonant Raman interaction with a strong angular-modulated control field in an extended $\ensuremath{\Lambda}$-type atomic ensemble. It is shown that effective multimode storage is possible when the Raman coherence spatial grating involves wave vectors with different longitudinal components relative to the paraxial signal field. The possibilities of implementing the scheme in the solid-state materials are discussed.

We study the coherent storage and retrieval of a very short multimode light pulse in an atomic ensemble. We consider a quantum memory process based on the conversion of a signal pulse into a long-lived spin coherence via light matter interaction in an on-resonant $\ensuremath{\Lambda}$ -type system. In order to study the writing and reading processes we analytically solve the partial differential equations describing the evolution of the field and of the atomic coherence in time as well as in space. We show how to optimize the process for writing as well as for reading. If the medium length is fixed, for each length, there is an optimal value of the pulse duration. We discuss the information capacity of this memory scheme and we estimate the number of transverse modes that can be stored as a quantum hologram.

Practical realizations of quantum repeaters require quantum memory simultaneously providing high retrieval efficiency, long lifetime and multimode storages. So far, the combination of high retrieval efficiency and spatially multiplexed storages into a single memory remains challenging. Here, we set up a ring cavity that supports an array including 6 TEM00 modes and then demonstrated cavity enhanced and spatially multiplexed spin wave photon quantum interface (QI). The cavity arrangement is according to Fermat' optical theorem, which enables the six modes to experience the same optical length per round trip. Each mode includesn horizontal and vertical polarizations. Via DLCZ process in a cold atomic ensemble, we create non classically correlated pairs of spin waves and Stokes photons in the 12 modes. The retrieved fields from the multiplexed SWs are enhanced by the cavity and the average intrinsic retrieval efficiency reaches 70% at zero delay. The storage time for the case that cross-correlation function of the multiplexed QI is beyond 2 reaches 0.6ms .

While several methods of information processing have been realized in quantum memories, thorough utilization of the spatial degree of freedom in highly-multimode memories demands a flexible method analogous to spatial light modulators (SLM) widely exploited in the broad field of optics to modulate the amplitude or phase of light. We want to present a spatial spin-wave modulator (SSM), allowing engineering of a spatial phase of spin-waves stored in a cold atomic memory. Using the SLM and polarizers we are able to shape a laser beam into an arbitrary shape. Such a prepared beam illuminates a cold rubidium cloud and due to ac-Stark effect the spatial phase of stored spin-waves is modified. The relative standard deviation of phase given by our SSM amounts to about 10%. We have also shown that losses scale quadratically with given phase. On one hand, that strongly limits the efficiency of SSM for strong phase modulation, but on the other hand enables efficient modulation in small range of several radians. During our research we have demonstrated a compensation of the quadratic phase introduced by a cylindrical lens placed in a readout path of our quantum memory. Moreover, introducing more complicated shapes of the ac-Stark beam, like saw or sine shape, we can shift and split spin-waves in Fourier domain [1]. Therefore we were able to interfere spin-waves stored in different spatial and temporal modes. This makes our SSM very robust tool which in conjugation with gradient echo memory can potentially allow to implement some new quantum protocols [2]. Finally, going to the single photon level we successfully observed a Hong-Ou-Mandel interference of two spin-waves stored in different spatial modes of our memory [3].