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Journal of Modern Optics

Phase gate for a photonic quantum network

Barbara Schallhart, Klaus M. Gheri

Published Nov 1, 2000• 0 citations
Publisher

Abstract

We give a fully quantum description of a simple model for a quantum phase gate which could be used for quantum communication in future optical quantum networks. The carriers of information are modelled as two-photon wavepackets which interact with an atom inside a two port cavity in a polarization-dependent manner. Owing to this interaction the different polarization states of the wavepackets suffer phase shifts which are intensity dependent. This process is well known as the Kerr effect.

DOI
10.1080/09500340008232181

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Physical Review A•Jun 5, 2007•50 citations
We give a fully quantum description of a simple model for a quantum phase gate which could be used for quantum communication in future optical quantum networks. The carriers of information are modelled as two-photon wavepackets which interact with an atom inside a two port cavity in a polarization-dependent manner. Owing to this interaction the different polarization states of the wavepackets suffer phase shifts which are intensity dependent. This process is well known as the Kerr effect.
We show that the optical Kerr effect can be used to construct a quantum phase gate. It is well known from quantum nondemolition techniques that, as two photon field modes pass through a Kerr medium, the phase of each mode will be shifted, and the size of the phase shift will depend on the number of photons in both modes. We discuss the Hamiltonian responsible for this effect and show how this can produce an effective photon-photon interaction which corresponds to the quantum phase gate operating on two qubits each of which is represented by the elliptical polarization of one photon field. We discuss decoherence and losses and suggest some methods for dealing with them.
We theoretically investigate the implementation of a quantum controlled-phase gate in a system constituted by a single atom inside an optical cavity, based on the electromagnetically induced transparency effect. First we show that a probe pulse can experience a $\ensuremath{\pi}$ phase shift due to the presence or absence of a classical control field. Considering the interplay of the cavity-EIT effect and the quantum memory process, we demonstrated a controlled-phase gate between two single photons. To this end, first one needs to store a (control) photon in the ground atomic states. In the following, a second (target) photon must impinge on the atom-cavity system. Depending on the atomic state, this second photon will be either transmitted or reflected, acquiring different phase shifts. This protocol can then be easily extended to multiphoton systems, i.e., keeping the control photon stored, it may induce phase shifts in several single photons, thus enabling the generation of multipartite entangled states. We explore the relevant parameter space in the atom-cavity system that allows the implementation of quantum controlled-phase gates using the recent technologies. In particular, we have found a lower bound for the cooperativity of the atom-cavity system which enables the implementation of phase shift on single photons. The induced shift on the phase of a photonic qubit and the controlled-phase gate between single photons, combined with optical devices, enable one to perform universal quantum computation.
Summary form only given. Achieving photon-photon interactions is one of the main objectives of the quantum information technology community, since these interactions provide the basis for deterministic quantum gates with high fidelity. In the last few years new milestones in creating phase-shifts [1] and quantum gates[2] have been achieved. Researching resource-moderate experimental realizations for the future development of this field provides a scalable framework for devices and opportunities for deployment in quantum communication networks.We highlight photon-photon interactions in unexplored physical regimes that are outside the standard approach of single atom QED or Rydberg transitions. Building on the first complete quantum optical characterization of an engineered free space phase shift triggered via atomic Kerr nonlinearities [3], we characterize novel architectures using the interaction of single photons in both a room temperature atomic vapor and cold atomic ensembles in miniaturized cavity QED setups. These different systems provide very compelling pathways to achieving photonphoton interactions.
In this dissertation, we shall focus on theoretically studying quantum nonlinear optical schemes to construct a conditional phase gate at the single-photon level. With an aim to develop analytical models, we shall carry out a rigorous quantized multimode field analysis of some of these schemes involving only the interacting field operators. More specifically, we shall first study the three-wave mixing process involving two single-photons in a second-order nonlinear medium (x(2)) under two different cases viz. when the photons are traveling with equal velocities and when they are traveling with different velocities, and explore the possibility of using them for building a conditional phase phase gate. Finally, we shall study the interaction of single-photon wavepackets with a realistic atomic system viz. an ensemble of five-level atoms, to construct a phase gate. We will particularly look at the "giant Kerr" effect in electromagnetically induced transparency to explore the possibility of using this scheme for achieving a conditional phase shift and to understand how the bandwidth gets restricted naturally in such an atomic system.
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.
We propose a scheme for realizing a two-qubit quantum phase gate between atoms inside a high-QQQ optical cavity. In the scheme, the dispersive interaction between atoms and the cavity field induces photon-number Stark shift, which can yield a resonant interaction inside one selected atom-field subspace and leave the others in a highly dispersive regime. Due to the selective atom-cavity interaction, (1) the scheme only requires commonly addressing the atoms inside the optical cavity during the gate operation, and (2) it can be directly used to implement an NNN-qubit conditional phase gate. These properties can significantly reduce the number of operations for implementing quantum computation and quantum algorithms.