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Laser Physics Letters

Quantum beats and wave mixing interactions in Raman systems: multimode squeezed and entangled states

Xing Li, Xiangming Hu

Published May 23, 2013• 5 citations
Publisher

Abstract

We describe the effects of Raman interactions on the quantum correlations of multimode optical fields. It is shown that both quantum beats and four-wave mixing processes exist in the Raman interactions of multimode fields with atomic reservoirs. These two mechanisms combine to lead to emission in pairs into multiple cavity modes. For four fields taken as examples, we find that the four-mode squeezed state can be created at steady state. From this we can obtain the Greenberger–Horne–Zeilinger entangled state, and the linear and square cluster entangled states. This scheme does not need the preparation of the initial states of atoms and cavity modes, and is robust against atomic spontaneous decay.

DOI
10.1088/1612-2011/10/7/075202

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We describe the effects of Raman interactions on the quantum correlations of multimode optical fields. It is shown that both quantum beats and four-wave mixing processes exist in the Raman interactions of multimode fields with atomic reservoirs. These two mechanisms combine to lead to emission in pairs into multiple cavity modes. For four fields taken as examples, we find that the four-mode squeezed state can be created at steady state. From this we can obtain the Greenberger–Horne–Zeilinger entangled state, and the linear and square cluster entangled states. This scheme does not need the preparation of the initial states of atoms and cavity modes, and is robust against atomic spontaneous decay.
We show that, in analogy to light fields, effective bosonic modes of atomic ensembles in the Holstein-Primakoff representation can be prepared in multimode squeezed states, and multipartite continuous-variable cluster and Greenberger-Horne-Zeilinger (GHZ) entangled states. Our scheme uses a cascade of optical cavities, in each of which one atomic ensemble is placed. Through Raman transitions between stable atomic ground states, the atomic ensembles are in the interactions with the cavity and laser fields. Because of the long-lived ground states, the atomic ensembles act as quantum network nodes, whose cluster entangled states are applicable in the one-way quantum computer, and whose GHZ entangled states have potential for quantum communication.
We present a collection of our recent schemes that have been proposed for continuous variable entanglement. Included in this collection are two types of optical systems. One is the four-wave mixing in resonantly or near-resonantly driven atomic systems. The numerical results and physical analyses are presented by using dressed atomic states and squeeze transformed cavity modes. Two dissipation channels are identified, through which the dressed atoms simultaneously absorb in the excitations from the pair of squeeze transformed modes. It is in the presence of such two channels that the entanglement is greatly enhanced and the best achievable state is the original Einstein-Podolsky-Rosen (EPR) entangled state. This scheme is applicable in the optical regime where atomic spontaneous emission has to be taken into account, unlike the two-step atomic reservoir engineering scheme, which is limited to the microwave regime. The other kind of systems is the quantum-beat laser with incoherent pump or coherent driving. Such a laser, when it operates well above threshold, produces entangled light. The numerical results and physical analyses are presented by using the collective modes of the lasing fields. The relative mode is decoupled from the active medium and thus remains in its vacuum state, while the sum mode operates well above threshold and displays sub-shot noise. The quantum-beat and the sum mode intensity noise reduction combine to yield entanglement between two bright beams and sub-Poissonian photon statistics of respective beams.
We propose a scalable scheme for a unitary multimode operator using an optical cavity with an atomic ensemble. We exemplify three-mode and four-mode cases and engineer the squeeze operators that are decoupled from the atomic degrees of freedom. The squeeze parameters can be large since they are proportional to the number of atoms. Using the input-output theory we show that ideal squeezed states and perfect squeezing could be approached at the output. At the same time, we show that it is possible to obtain tripartite and quadripartite Greenberger-Horne-Zeilinger entangled states for continuous variables. The responsible mechanism for both the multimode squeezing and the genuine multipartite entanglement is based on the atomic coherence controlled parametric interactions. The scalability of the scheme is simply obtained by including more transitions in the atomic system.
In this paper, we investigate the generation of multimode entanglement and squeezing of an optical field via coupled four-wave mixing interactions in a Kerr nonlinear medium pumped at multiple well-separated frequencies. We show that genuine multimode entanglement can be obtained and this entanglement can be verified with the measurable multimode squeezing present in the system. This scheme may be used to achieve entangled frequency combs which are useful in continuous-variable quantum communication networks.
We analyze quantum correlations in four-wave mixing in three-level $\ensuremath{\Lambda}$ and V atomic systems by using dressed atomic states and squeeze-transformed cavity modes. Two dissipation channels are identified, through which the dressed atoms simultaneously absorb in the excitations from the pair of squeeze-transformed modes. It is in the presence of two channels that the entanglement is greatly enhanced and the best achievable state approaches the original Einstein-Podolsky-Rosen entangled state. This scheme is applicable in the optical regime where atomic spontaneous emission has to be taken into account, unlike the two-step atomic reservoir engineering scheme, which is limited to the microwave regime.