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arXiv:1702.05959 · Journal of Physics B Atomic Molecular and Optical Physics

Optimal control for perfect state transfer in linear quantum memory

Hideaki Nakao, Naoki Yamamoto

Published Feb 16, 2017• 9 citations
arXivHTMLPDF

Abstract

Abstract A quantum memory is a system that enables transfer, storage, and retrieval of optical quantum states by ON/OFF switching of the control signal in each stage of the memory. In particular, it is known that, for perfect transfer of a single-photon state, appropriate shaping of the input pulse is required. However, in general, such a desirable pulse shape has a complicated form, which would be hard to generate in practice. In this paper, for a wide class of linear quantum memory systems, we develop a method that reduces the complexity of the input pulse shape of a single photon while maintaining the perfect state transfer. The key idea is twofold; (i) the control signal is allowed to vary continuously in time to introduce an additional degree of freedom, and then (ii) an optimal control problem is formulated to design a simple-formed input pulse and the corresponding control signal. Numerical simulations are conducted for Λ-type atomic media and networked atomic ensembles, to show the effectiveness of the proposed method.

DOI
10.1088/1361-6455/aa5257

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Abstract A quantum memory is a system that enables transfer, storage, and retrieval of optical quantum states by ON/OFF switching of the control signal in each stage of the memory. In particular, it is known that, for perfect transfer of a single-photon state, appropriate shaping of the input pulse is required. However, in general, such a desirable pulse shape has a complicated form, which would be hard to generate in practice. In this paper, for a wide class of linear quantum memory systems, we develop a method that reduces the complexity of the input pulse shape of a single photon while maintaining the perfect state transfer. The key idea is twofold; (i) the control signal is allowed to vary continuously in time to introduce an additional degree of freedom, and then (ii) an optimal control problem is formulated to design a simple-formed input pulse and the corresponding control signal. Numerical simulations are conducted for Λ-type atomic media and networked atomic ensembles, to show the effectiveness of the proposed method.
In this paper, we study a general linear networked system that contains a tunable memory subsystem; that is, it is decoupled from an optical field for state transportation during the storage process, while it couples to the field during the writing or reading process. The input is given by a single photon state or a coherent state in a pulsed light field. We then completely and explicitly characterize the condition required on the pulse shape achieving the perfect state transfer from the light field to the memory subsystem. The key idea to obtain this result is the use of zero-dynamics principle, which in our case means that, for perfect state transfer, the output field during the writing process must be a vacuum. A useful interpretation of the result in terms of the transfer function is also given. Moreover, a four-node network composed of atomic ensembles is studied as an example, demonstrating how the input field state is transferred to the memory subsystem and what the input pulse shape to be engineered for perfect memory looks like.
Optical quantum memory, the ability to store photonic quantum states and retrieve them on demand, is an essential resource for emerging quantum technologies and photonic quantum information protocols. Simultaneously achieving high efficiency and high-speed, broadband operation is an important task necessary for enabling these applications. We investigate the optimization of a large class of optical quantum memories based on resonant and near-resonant interaction with ensembles of $\mathrm{\ensuremath{\Lambda}}$-type level systems with the restriction that the temporal envelope of all optical fields must be Gaussian, which reduces experimental complexity. Through this optimization we demonstrate an experimentally simple path to saturation of the protocol-independent storage efficiency bound that is valid for a wide range of memory bandwidths, including those that are broadband and high speed. Examining the resulting optimal Gaussian control field parameters, we find a continuous transformation between three physically distinct resonant quantum memory protocols. We compare this Gaussian optimization scheme with standard shape-based optimization.
Ideal photonic quantum memories can store arbitrary pulses of light with unit efficiency. This requires operating in the adiabatic regime, where pulses have a duration much longer than the bandwidth of the memory. In the nonadiabatic regime of short pulses, memories are therefore imperfect, and information is always lost. We theoretically investigate the bandwidth limitations for setups based on individual atoms, or ensembles thereof, confined inside optical cavities. We identify an effective strategy for optimizing the efficiencies of the storage and retrieval process regardless of the duration or the shape of the pulses. Our protocol is derived almost completely analytically and attains efficiencies that are comparable to those obtained by numerical optimization. Furthermore, our results provide an improved understanding of the performance of quantum memories in several regimes. When considering pulses defined on an infinite time interval, the shapes can be divided into two categories, depending on their asymptotic behaviors. If the intensity of the pulse increases with time slower than or as an exponential function then the storage efficiency is only limited by the pulse width. For pulses defined on a finite interval, on the other hand, the efficiency is determined by the shape at the beginning of the storage or, correspondingly, at the end of the retrieval process.
Optical quantum memory--the ability to store photonic quantum states and retrieve them on demand--is an essential resource for emerging quantum technologies and photonic quantum information protocols. Simultaneously achieving high efficiency and high-speed, broadband operation is an important task necessary for enabling these applications. In this work, we investigate the optimization of a large class of optical quantum memory protocols based on resonant interaction with ensembles of Λ\LambdaΛ-type level systems with the restriction that the temporal envelope of all optical fields must be Gaussian, which reduces experimental complexity. We show that for overlapping signal and control fields there exists a unique and broadband pulse duration that optimizes the memory efficiency, and that this optimized efficiency can be close to the protocol-independent bound. We further optimize over the control field temporal delay and pulse duration, demonstrating saturation of this efficiency bound over a broad range of pulse durations while clarifying the underlying physics of the quantum memory interaction.
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.
We propose a dynamical approach to quantum memories using an oscillator-cavity model. This overcomes the known difficulties of achieving high quantum input-output fidelity with long storage times compared to the input signal duration. We use a generic model of the memory response, which is applicable to any linear storage medium ranging from a superconducting device to an atomic medium. The temporal switching or gating of the device may either be through a control field changing the coupling, or through a variable detuning approach, as in more recent quantum memory experiments. An exact calculation of the temporal memory response to an external input is carried out. This shows that there is a mode-matching criterion which determines the optimum input and output pulse time evolution. This optimum pulse shape can be modified by changing the gate characteristics. In addition, there is a critical coupling between the atoms and the cavity that allows high fidelity in the presence of long storage times. The quantum fidelity is calculated both for the coherent state protocol, and for a completely arbitrary input state with a bounded total photon number. We show how a dynamical quantum memory can surpass the relevant classical memory bound, while retaining long storage times.