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arXiv:1403.1698 · New Journal of Physics

Zero-dynamics principle for perfect quantum memory in linear networks

Naoki Yamamoto, M. R. James

Published Jul 23, 2014• 48 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/16/7/073032

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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.
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 show that quantum memory for qudit states encoded in a single photon pulsed optical field has a conceptually simple modular realization using only passive linear optics and coherent feedback. We exploit the idea that two decaying optical cavities can be coupled in a coherent feedback configuration to create an internal mode of the coupled system which is isolated and decoherence-free for the purpose of qubit storage. The qubit memory can then be switched between writing/read-out mode and storage mode simply by varying the routing of certain freely propagating optical fields in the network. It is then shown that the qubit memories can be interconnected with one another to form a qudit quantum memory. We explain each of the phase of writing, storage, and read-out for this modular quantum memory scheme. The results point a way towards modular architectures for complex compound quantum memories.
In this paper, we show that quantum memory for qudit states encoded in a single photon pulsed optical field has a conceptually simple modular realization using only passive linear optics and coherent feedback. We exploit the idea that two decaying optical cavities can be coupled in a coherent feedback configuration to create an internal mode of the coupled system which is isolated and decoherence-free for the purpose of qubit storage. The qubit memory can then be switched between writing/read-out mode and storage mode simply by varying the routing of certain freely propagating optical fields in the network. It is then shown that the qubit memories can be interconnected with one another to form a qudit quantum memory. We explain each of the phase of writing, storage, and read-out for this modular quantum memory scheme. The results point a way towards modular architectures for complex compound quantum memories.
Abstract Attenuated laser pulses are often employed in place for single photons in order to test the efficiency of the elements of a quantum network. In this work we analyze theoretically the dynamics of storage of an attenuated light pulse (where the pulse intensity is at the single photon level) propagating along a transmission line and impinging on the mirror of a high finesse cavity. Storage is realized by the controlled transfer of the photonic excitations into a metastable state of an atom confined inside the cavity and occurs via a Raman transition with a suitably tailored laser pulse, which drives the atom and minimizes reflection at the cavity mirror. We determine the storage efficiency of the weak coherent pulse which is reached by protocols optimized for single-photon storage. We determine the figures of merit and we identify the conditions on an arbitrary pulse for which the storage dynamics approaches the one of a single photon. Our formalism can be extended to arbitrary types of input pulses and to quantum memories composed by spin ensembles, and serves as a basis for identifying the optimal protocols for storage and readout.
We propose a quantum network consisting of optical waveguides in the linear regime for quantum state transfer. The circular topology of our network introduces novel functionalities that enable us to analytically identify the conditions under which perfect state transfer (PST) is achievable. We utilize the properties of the Fourier modes, in particular the zero Fourier modes, which provide a protected subspace for the efficient propagation of quantum states, resulting in PST to the diametrically opposite site in a network with any number of sites N=4nN = 4nN=4n. The coupling profiles in the photonic network modulate the number of zero-energy eigenmodes, with uniform couplings yielding more than evanescent ones, confirming that the expedition of observed PST originates from the collapse of the eigenvalue spectrum into three distinct eigenvalue blocks, including N/2N/2N/2 manifolds of zero Fourier modes. We investigate PST in both discrete- and continuous-variable input regimes, using single photon state, Schrödinger cat states, and two-mode squeezed vacuum state. Our findings apply to the engineering of quantum networks and photonic lattices, paving the way for applications in controlled routing in integrated quantum circuits.