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Journal of the Optical Society of America B

Creation of an unequally weighted four-mode square cluster state in a ring cavity

Yan Yan, Ge Huang, Zhidong Zhou, Gao‐xiang Li

Published May 29, 2019• 0 citations
Publisher

Abstract

Four-mode continuous-variable (CV) cluster states are an important and necessary resource in continuous-variable quantum computation. In this paper, we present a simple and efficient scheme to realize an unequally weighted four-mode square CV cluster state using atomic ensembles driven by seven strong classical laser fields. The scheme requires just a single selection of the appropriate squeezing parameters and pump laser parameters. With the unique squeezing operator and a new unitary transformation, we show that seven laser fields drive four atomic ensembles into a stationary four-mode squeezed vacuum state via the cavity dissipation.

DOI
10.1364/josab.36.001700

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Four-mode continuous-variable (CV) cluster states are an important and necessary resource in continuous-variable quantum computation. In this paper, we present a simple and efficient scheme to realize an unequally weighted four-mode square CV cluster state using atomic ensembles driven by seven strong classical laser fields. The scheme requires just a single selection of the appropriate squeezing parameters and pump laser parameters. With the unique squeezing operator and a new unitary transformation, we show that seven laser fields drive four atomic ensembles into a stationary four-mode squeezed vacuum state via the cavity dissipation.
A practical scheme is proposed for the creation of continuous-variable entangled cluster states of four distinct atomic ensembles located inside a high-finesse ring cavity. The scheme does not require a set of external input squeezed fields, a network of beam splitters, and measurements. It is based on nothing else than the dispersive interaction between the atomic ensembles and the cavity mode and a sequential application of laser pulses of a suitably adjusted amplitudes and phases. We show that the sequential laser pulses drive the atomic ``field modes'' into pure squeezed vacuum states. The state is then examined against the requirement to belong to the class of cluster states. We illustrate the method on three examples of the entangled cluster states: the so-called continuous-variable linear, square, and T-type cluster states.
Two schemes for the preparation of weighted continuous variable cluster states with four atomic ensembles are proposed. In the first scheme, the four separated atomic ensembles inside a two-mode ring cavity are driven by pulse laser fields. The basic idea of the scheme is to transfer the ensemble bosonic modes into suitable linear combinations that can be prepared in a pure cluster state by a sequential application of the laser pulses with the aid of the cavity dissipation. In the second one, we take two separate two-mode cavities, each containing two atomic ensembles. The distant cavities are coupled by dissipation in a cascade way. It has been found that the mixed cluster state can be produced. These schemes may contribute towards implementing continuous variable quantum computation, quantum communication and networking based on atomic ensembles.
We propose an experimental scheme that has the potential for large-scale realization of continuous-variable (CV) cluster states for universal quantum computation. We do this by mapping CV cluster-state graphs onto two-mode squeezing graphs, which can be engineered into a single optical parametric oscillator (OPO). The desired CV cluster state is produced directly from a joint squeezing operation on the vacuum, using a multifrequency pump beam. This method has potential for ultracompact experimental implementation. As an illustration, we detail an experimental proposal for creating a four-mode square CV cluster state with a single OPO.
We propose a scheme to generate four-mode cluster states with four atomic ensembles trapped in single-mode cavities connected by short fibers. With the aid of the cavity dissipation, we find that a four-mode cluster state can be unconditionally created by the simultaneous driving of the ensembles with laser pulses of suitably chosen Rabi frequencies and phases. The scheme could be easily extended to the case of NNN-mode cluster states.
We consider a chain of six coupled single-mode cavities, each containing an ensemble of four-level atoms, and demonstrate how to prepare stationary six-mode cluster states of the atomic ensembles. We show that a six-mode cluster state can be created in a single step by driving the ensembles with laser pulses of suitably chosen Rabi frequencies and phases. Introducing linear superpositions of the collective bosonic modes of the atomic ensembles, we show that the superposition modes can independently evolve to a desired stationary state with the help of the cavity damping. We illustrate this method by examining three examples of the creation of linear, hexagon, and double square cluster states.