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Physical Review A

Storage and retrieval of time-bin qubits with photon-echo-based quantum memories

Nicolas Gisin, Sergey A. Moiseev, Christoph Simon

Published Jul 9, 2007• 24 citations
Publisher

Abstract

Quantum memories based on the photon-echo principle (with controlled reversible inhomogeneous broadening) allow in principle perfect reconstruction of the stored light. In the retrieval process, the envelope of the absorbed wave packet is reversed in time, but the evolution of the phase of the carrier wave is unchanged. We discuss the consequences of this fact for the relative phase of pulses with a certain time delay, and thus for the storage of time-bin qubits. As an illustration, we show that the combination of photon-echo-based memories and unbalanced interferometers leads to a counterintuitive interference effect, allowing one to measure a path length difference $\ensuremath{\Delta}L$ using pulses that are much shorter than $\ensuremath{\Delta}L$.

DOI
10.1103/physreva.76.014302

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Physical Review A•Jun 24, 2010•38 citations
Quantum memories based on the photon-echo principle (with controlled reversible inhomogeneous broadening) allow in principle perfect reconstruction of the stored light. In the retrieval process, the envelope of the absorbed wave packet is reversed in time, but the evolution of the phase of the carrier wave is unchanged. We discuss the consequences of this fact for the relative phase of pulses with a certain time delay, and thus for the storage of time-bin qubits. As an illustration, we show that the combination of photon-echo-based memories and unbalanced interferometers leads to a counterintuitive interference effect, allowing one to measure a path length difference \ensuremathΔL\ensuremath{\Delta}L\ensuremathΔL using pulses that are much shorter than \ensuremathΔL\ensuremath{\Delta}L\ensuremathΔL.
We develop the theory of an optical quantum memory protocol based on the three pulse photon echo (PE) in an optically dense medium with controlled reversible inhomogeneous broadening (CRIB). The wave-function of the retrieved photon echo field is derived explicitly as a function of an arbitrary input Data light field. The storage and retrieval of time-bin qubit states based on the described quantum memory is discussed, and it is shown that the memory allows to measure the path length difference in an imbalanced interferometer using short light pulses.
We have developed a quantum memory using quantum dots with a photon echo method for the storage of ultraweak femtosecond pulses. This quantum memory has a large bandwidth of 7.2 THz, which can be achieved due to the large inhomogeneous broadening of quantum dots. We successfully demonstrated femtosecond timebin pulse transfer to photon-echo-based quantum memory using quantum dots. We also succeeded in measuring the retrieved time-bin pulses as a photon echo from the quantum memory using a pulse-pumped frequency upconversion single-photon detector (UCSPD) with a temporal resolution of 429 fs. It is found that the retrieved time-bin photon echo pulse maintains the sub-picosecond time duration and the relative phase.
Photon-echo-based quantum memories use inhomogeneously broadened, optically thick ensembles of absorbers to store a weak optical signal and employ various protocols to rephase the atomic coherences for information retrieval. We study the application of two consecutive, frequency-chirped control pulses for coherence rephasing in an ensemble with a ``natural'' inhomogeneous broadening. Although propagation effects distort the two control pulses differently, chirped pulses that drive adiabatic passage can rephase atomic coherences in an optically thick storage medium. Combined with spatial phase-mismatching techniques to prevent primary echo emission, coherences can be rephased around the ground state to achieve secondary echo emission with close to unit efficiency. Potential advantages over similar schemes working with $\ensuremath{\pi}$ pulses include greater potential signal fidelity, reduced noise due to spontaneous emission, and better capability for the storage of multiple memory channels.
We report experimental storage and retrieval of weak coherent states of light at telecommunication wavelengths using erbium ions doped into a solid. We use two photon-echo-based quantum storage protocols. The first one is based on controlled reversible inhomogeneous broadening (CRIB). It allows the retrieval of the light on demand by controlling the collective atomic coherence with an external electric field, via the linear Stark effect. We study how atoms in the excited state affect the signal-to-noise ratio of the CRIB memory. Additionally we show how CRIB can be used to modify the temporal width of the retrieved light pulse. The second protocol is based on atomic frequency combs. Using this protocol we verify that the reversible mapping is phase preserving by performing an interference experiment with a local oscillator. These measurements are enabling steps toward solid-state quantum memories at telecommunication wavelengths. We also give an outlook on possible improvements.
The non-interacting and high-speed nature of light makes it an ideal carrier of information that is essential for transmission of quantum information. Indeed, many proposals and demonstrations of quantum cryptography rely on the use of fibre-optic networks. Construction of a memory that can store light and preserve its quantum properties will be useful in a range of quantum information systems such as secure quantum communication and quantum computation. This is why a quantum memory for light is a remarkable objective. The key to quantum memory is to store the probability amplitude of the possible outcomes of measurement but without measurement. An important criterion for a quantum memory is that the efficiency of the recall must exceed 50%. This is the crucial no-cloning limit for security of information, since it guarantees that nobody can access the information by copying it. This benchmark is important because any kind of deterministic amplification of quantum information is fundamentally impossible. On-demand retrieval of information and ability to controllably manipulate the quantum information are also important for quantum applications. When light is absorbed by atoms, it is actually possible to reverse the absorption process. In our memory system: light is absorbed by an ensemble of atoms and, using careful conditioning and control, we can cause the stored light to be regenerated and released at a later time. This is done by applying a gradient of magnetic field along the atomic ensemble that is the basis for our optical memory. To recall the light we flip the sign of the gradient field. This kind of reversible absorption is called photon echo, hence the name of our scheme: The Gradient Echo Memory (GEM). This simple protocol is used in our experiment and can be applied to a range of different atomic systems. We have extended the GEM protocol and experimentally implemented a memory using three-level atoms. We used an off-the-shelf Rb vapour cell operating above room temperature as the memory medium. In this realisation, we broke the efficiency record with 87% recall of the input light pulse. Moreover, through complete state tomography of coherent states we have demonstrated the ability of our memory to noiselessly store quantum states of light. We have also demonstrated that the memory can store a string of pulses and then recall the pulses ondemand in arbitrary order allowing re-sequencing of the stored information. Furthermore, we have shown that pulses could be time-compressed, time-stretched or split into multiple smaller pulses and selectively recalled in several pieces. This technique enables the construction of an optical random-access memory for quantum information. Moreover, the scheme to manipulate the spectral properties of optical data, stored inside the memory, has been introduced. We have also investigated the possibility of obtaining large nonlinear phase shifts between single photons inside the memory. Such strong interactions can be used for the implementation of universal quantum gates.
The three-pulse photon echo is a well-known technique to store intense light pulses in an inhomogeneously broadened atomic ensemble. This protocol is attractive because it is relatively simple and it is well suited for the storage of multiple temporal modes. Furthermore, it offers very long storage times, greater than the phase relaxation time. Here, we consider the three-pulse photon echo in both two- and three-level systems as a potential technique for the storage of light at the single-photon level. By explicit calculations, we show that the ratio between the echo signal corresponding to a single-photon input and the noise is smaller than one. This severely limits the achievable fidelity of the quantum state storage, making the three-pulse photon echo unsuitable for single-photon quantum memory.