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arXiv:1111.4261 · Physical Review A

Quantum memory with a single two-level atom in a half cavity

Yimin Wang, Jiří Minář, Gabriel Hetet, Valerio Scarani

Published Jan 18, 2012• 21 citations
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Abstract

We propose a setup for quantum memory based on a single two-level atom in a half cavity with a moving mirror. We show that various temporal shapes of incident photon can be efficiently stored and read out by shaping the time-dependent decay rate $\ensuremath{\gamma}(t)$ between the atom and the light. This is achieved uniquely by an appropriate motion of the mirror without the need for additional control laser or atomic level. We present an analytical expression for the efficiency of the process and study its dependence on the ratio between the incident light field bandwidth and the atomic decay rate. We discuss possible implementations and experimental issues, particularly for a single atom or ion in a half cavity quantum optical setup as well as a superconducting qubit in the context of circuit QED.

DOI
10.1103/physreva.85.013823

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We propose a setup for quantum memory based on a single two-level atom in a half cavity with a moving mirror. We show that various temporal shapes of incident photon can be efficiently stored and read out by shaping the time-dependent decay rate \ensuremathγ(t)\ensuremath{\gamma}(t)\ensuremathγ(t) between the atom and the light. This is achieved uniquely by an appropriate motion of the mirror without the need for additional control laser or atomic level. We present an analytical expression for the efficiency of the process and study its dependence on the ratio between the incident light field bandwidth and the atomic decay rate. We discuss possible implementations and experimental issues, particularly for a single atom or ion in a half cavity quantum optical setup as well as a superconducting qubit in the context of circuit QED.
Quantum information processing tasks have been implemented in various physical platforms. In this thesis, we consider two specific implementations: Part I presents a detailed study of the interaction of a single atom with a light pulse. Part II examines the case of a quantum controlled-phase gate in circuit quantum electrodynamics in the ultrastrong coupling regime. They are both actively pursued by many research groups. In Part I, we first present the framework for a single two-level atom interacting with the quantized electromagnetic field. The effect of temporal and spectral properties of the pulses on atomic excitation is studied for both Fock state and coherent state pulse. The detailed analysis of atomic excited state population is provided for single photon pulse with various temporal shapes. The work is then extended to a more general case with two spatial-modes and multi-photon pulses. The difference between Fock state and coherent state pulse on atomic excitation is further investigated. We find that at few photon levels, the maximum atomic excitation probability is a monotonic function of photon number for the coherent state pulse, but not for the Fock state pulse. Furthermore, we show that the atomic dynamics can be controlled by the initial relative phase between the two counter-propagating coherent state pulses incident on the atom, which is not the case with two Fock state pulses. The theoretical prediction is then compared with an experiment, where a single trapped 87Rb atom interacts with coherent state pulses engineered in temporal shape of rising exponential and rectangular form. Next, we propose a quantum memory setup based on a single two-level atom in a half cavity with a moving mirror. The efficiency of the quantum storage process is studied analytically and
We theoretically studied the implementation of a quantum memory and an optical transistor in a system composed by a single atom trapped inside a high finesse cavity. In order to store and map the quantum state of an input pulse onto internal states of the single atom (quantum memory) we employ the electromagnetically induced transparency (EIT) phenomenon (which can work out as an optical transistor) where the information can be transferred to the dark state of the atom modelled by a three-level system in a Λ-type configuration. In our model we consider a suitable temporal shape for the control field that ensures the adiabaticity of the storage process and retrieval of the probe pulse. The dynamic of the field inside the cavity was obtained by master equation approach, while the outside field was calculated by input-output formalism. We have analysed two different setups: i) two-sided and ii) single-sided cavities. While the first setup is the most appropriate and commonly used to observe cavity-EIT in the transmission spectrum, thus the best configuration for the optical transistor, the maximum quantum memory efficiency can not reach reasonable values, being limited to 50% for symmetric cavities. On the other hand, with single-sided cavity the quantum memory efficiency increases considerably and can reach values close to 100% in the strong atom-field coupling regime. However this specific setup is not favourable to observe the cavity-EIT effect in the transmission spectrum and then it is not appropriate to control the transmission of light pulses.
We show how to capture a single photon of arbitrary temporal shape with one atom coupled to an optical cavity. Our model applies to Raman transitions in three-level atoms with one branch of the transition controlled by a (classical) laser pulse, and the other coupled to the cavity. Photons impinging on the cavity normally exhibit partial reflection, transmission, and/or absorption by the atom. Only a control pulse of suitable temporal shape ensures impedance matching throughout the pulse, which is necessary for complete state mapping from photon to atom. For most possible photon shapes, we derive an unambiguous analytic expression for the shape of this control pulse, and we discuss how this relates to a quantum memory.
Here we show that the photon echo equivalent of an NMR gradient echo is completely efficient if the sample is optically thick, the detunings of the atoms vary linearly along the direction of propagation and the storage time is short compared to the decay rate of the atoms. In this process the only light that interacts with the sample of atoms during the storage and retrieval process is the light that is to be stored and then retrieved, their are no auxiliary beams. The stored and recalled light travel in the same direction and their is no need for the phase matching operation that is present in previous quantum memory proposals using controlled inhomogeneous broadening. This greatly simplifies various possible implementations. We present analytical, numerical and experimental results of this scheme. We report experimental efficiencies of up to 15% and suggest simple realizable improvements to significantly increase the efficiency.
The behavior of a two-level atom in a half-cavity, i.e., a cavity with one mirror, is studied within the framework of a one-dimensional model with respect to spontaneous decay and resonance fluorescence. The system under consideration corresponds to the setup of a recently performed experiment [J. Eschner et al., Nature (London) 413,413,413, 495 (2001)] where the influence of a mirror on a fluorescing single atom was revealed. In the present work special attention is paid to the regime of large atom-mirror distances where intrinsic memory effects can not longer be neglected. This is done with the help of delay-differential equations which contain, for small atom-mirror distances, the Markovian limit with effective level shifts and decay rates leading to the phenomenon of enhancement or inhibition of spontaneous decay. Several features are recovered beyond an effective Markovian treatment, appearing in experimentally accessible quantities like the intensity or emission spectra of the scattered light.
We theoretically analyze the efficiency of a quantum memory for single photons. The photons propagate along a transmission line and impinge on one of the mirrors of a high-finesse cavity. The quantum memory is constituted by a single atom within the optical resonator. Photon storage is realized by the controlled transfer of the photonic excitation into a metastable state of the atom and occurs via a Raman transition with a suitably tailored laser pulse, which drives the atom. Our study is supported by numerical simulations, in which we include the modes of the transmission line and we use the experimental parameters of existing experimental setups. It reproduces the results derived using input–output theory in the corresponding regimes and can be extended to compute dynamics where the input–output formalism cannot be straightforwardly applied. Our analysis determines the maximal storage efficiency, namely, the maximal probability to store the photon in a stable atomic excitation, in the presence of spontaneous decay and cavity parasitic losses. It further delivers the form of the laser pulse that achieves the maximal efficiency by partially compensating parasitic losses. We numerically assess the conditions under which storage based on adiabatic dynamics is preferable to non-adiabatic pulses. Moreover, we systematically determine the shortest photon pulse that can be efficiently stored as a function of the system parameters.