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arXiv:1102.3266

Quantum logical gates operating on stored light

Karolina Słowik, Andrzej Raczyński, Jarosław Zaremba, S. Zielińska-Kaniasty

Published Feb 16, 2011• 0 citations
arXivHTMLPDF

Abstract

An implementation is proposed of single qubit gates, e.g., phase, NOT, \sqrt{NOT} and Hadamard, operating on polarized photons and based on light storage. Instead of processing photons themselves, qubit transformations are performed on atomic excitations due to photon storage in a medium of atoms in the tripod configuration.
DOI
10.48550/arxiv.1102.3266

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Quantum gates are fundamental in Quantum computing for their role in manipulating elementary information carriers referred to as quantum bits. In this paper, a theoretical scheme for realizing a quantum Hadamard and a quantum controlled-NOT logic gates operations in the anti-Jaynes-Cummings interaction process is provided. Standard Hadamard operation for a specified initial atomic state is achieved by setting a specific sum frequency and photon number in the normalized anti-Jaynes-Cummings qubit state transition operation with the interaction component of the anti-Jaynes-Cummings Hamiltonian generating the state transitions. The quantum controlled-NOT logic gate is realized when a single atomic qubit defined in a two-dimensional Hilbert space is the control qubit and two non-degenerate and orthogonal polarized cavities defined in a two-dimensional Hilbert space make the target qubit. With precise choice of interaction time in the anti-Jaynes-Cummings qubit state transition operations defined in the anti-Jaynes-Cummings sub-space spanned by normalized but non-orthogonal basic qubit state vectors, ideal unit probabilities of success in the quantum controlled-NOT operations is determined.
Much of the current understanding of logic gates for quantum computation relies on the application of one- and two-qubit gates in order to implement a universal set of logic gates, as well as other gates. Such ideas stem from the notion that the Hamiltonians available for quantum computation are one or two-body processes. However, present day NMR implementations of quantum information processing (QIP) rely on the internal Hamiltonian of a liquid state system in which there are many two-body processes that occur simultaneously. Such use of the internal Hamiltonian allows for the creation of `multiqubit' logic gates, i.e. logic gates that operate on many qubits simultaneously and are more efficient than a sequence of one- and two-qubit rotations that effect the same operation. Such larger qubit operations offer a universal set of gates (even when not all couplings within the internal Hamiltonian are readily accessible) as well as more convenient and efficient implementations of the Hadamard transform, the controlled-NOT gate, and a quantum Fourier transform that scales linearly (assuming all couplings can be turned on and off at will).
It is known that photons are the ideal carriers of quantum information and ensemble of atoms can be acted as the long lived storage and processing units. In the coherently prepared atomic ensemble with the light resonantly interacting with the atoms, various schemes have been proposed to implement quantum state transfer and storage, quantum phase gate, generation of entangled photons, and the long-distance quantum communication [1]. We first proposed the dark-state polaritons in a five-level M-type atomic ensemble in the electro magnetically induced transparency (EIT) [2], Under conditions of the low excitation limit and adiabatic following, the quantum field can be mapped onto the atomic polarization states, forming the shape preserving quantum states of polaritons. Two channels for robust quantum memory are provided. Then, we investigated the nonlinear optical response of a five-level tripod atomic system in the EIT, and proposed a three-qubit phase gate protocol based on the fifth-order nonlinearity [3]. The cross phase modulation among three weak fields induced by the fifth-order nonlinearity in EIT can produce the phase shift of order n, which can be used to realize the three-qubit polarization phase gate. Finally, we proposed a cavity-QED scheme that can effectively generate EPR polarization-entangled photon pairs [4], A four-level tripod atom successively couples to two high-Q optical cavities possessing polarization degeneracy, assisted by a classical π-polarized pump field. The stimulated Raman adiabatic passage process in the atom-cavity system is used to produce the polarization-entangled photon pairs. The proposal is particularly robust against atomic spontaneous decay. The above protocols should have potential applications in quantum information processing.
Light propagation and storing in a medium of atoms in the tripod configuration driven by two control pulses are investigated theoretically in terms of two polaritons and numerically. It is shown that a magnetic field switched on at the pulse storage stage changes the phase relations between the atomic coherences due to the stored pulse, which leads to an essential modification of the released pulse. Quantitative relations concerning the released pulse and the coherences are given. A general situation when the two control fields are not proportional at the pulse release stage is also examined. It is shown that in both cases a single dark state polariton is not sufficient to account for the pulse evolution, which is connected with the fact that a part of the signal remains in the medium after the release stage.