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ACTA PHOTONICA SINICA

Frequency Up- and Down-conversions in Two-mode Cavity

李斌 Li Bin, 冯勋立 FENG Xun-li, 张智明 Zhang Zhiming

Published Jan 1, 2011• 1 citation

Abstract

A scheme was proposed to construct bilinear and quadratic Hamiltonians for frequency up-and down-conversions in cavity quantum electrodynamics(QED).Generally,in nonlinear optics,the interaction that the energe swaps between different optic modes without atomic transition is named frequency conversion.The proposed scheme was based on the interactions of a single four-level atom simultaneously with two classical driving fields and a two-mode cavity field,which is in the domain of four-wave mixing.By initially preparing the atom in a suitable state,each pump light was resonant with its transition,and two quantum modes were large tune to the other two transition,respectively,In the strong laser regime,the atomic degrees of freedom could be decoupled from the cavity degrees of freedom and the frequency conversion could be realized for the cavity modes.Due to the different initial states and interactions between optic fields and atom,frequency up-and down-conversions arose,respectively.After the preparation of squeezed operation respect to Frequency down-conversion,a discussion on the feasibility of experiment was given and the theoretical value was obtained.The advantage of this proposal is to realize the transition using two cascade photons,which is dipole-forbidden in a cascade structure atom,with high efficiency.The proposal will be useful for optical quantum control and fundamental tests of quantum theory.

DOI: 10.3788/gzxb20114008.1161

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A scheme was proposed to construct bilinear and quadratic Hamiltonians for frequency up-and down-conversions in cavity quantum electrodynamics(QED).Generally,in nonlinear optics,the interaction that the energe swaps between different optic modes without atomic transition is named frequency conversion.The proposed scheme was based on the interactions of a single four-level atom simultaneously with two classical driving fields and a two-mode cavity field,which is in the domain of four-wave mixing.By initially preparing the atom in a suitable state,each pump light was resonant with its transition,and two quantum modes were large tune to the other two transition,respectively,In the strong laser regime,the atomic degrees of freedom could be decoupled from the cavity degrees of freedom and the frequency conversion could be realized for the cavity modes.Due to the different initial states and interactions between optic fields and atom,frequency up-and down-conversions arose,respectively.After the preparation of squeezed operation respect to Frequency down-conversion,a discussion on the feasibility of experiment was given and the theoretical value was obtained.The advantage of this proposal is to realize the transition using two cascade photons,which is dipole-forbidden in a cascade structure atom,with high efficiency.The proposal will be useful for optical quantum control and fundamental tests of quantum theory.

We propose experimental schemes for realizing frequency up- and down-conversion in two-mode cavity QED by considering the atom-cavity interaction in the presence of a strong driving classical field. In contrast to the recent paper based on dispersive atom-cavity interaction [Serra et al., Phys. Rev. A 71, 045802 (2005)], our scheme is based on resonant interaction of the cavity modes with a single driven three-level atom, so that the quantum dynamics operates at a high speed, which is important in view of decoherence. It is shown that, with the help of a strong driving classical field, frequency up- and down-conversion operations can be realized by initially preparing the atom in a certain state.

Using a strong driving classical field, we propose experimental schemes for realizing frequency up-and down-conversion in a two-mode cavity by an artificial atom with cyclic population transfer. Our scheme is based on resonant interaction of the cavity modes with a single driven three-level artificial atom, so that the quantum dynamic operation is at a high speed, which is important in view of decoherence. It is shown that frequency up- and down-conversion operations can be realized by initially preparing the artificial atom in a certain state. As an application, we show how to generate a two-mode squeezed state from any initially field state in the cavity.

A scheme is presented for realizing frequency-up conversion and a two-qubit quantum swap gate for intracavity fields. In the scheme, a V-type atomic ensemble prepared in their ground states collectively mediates the interaction between the two cavity modes. Under certain conditions, the cavity-field degree of freedom is decoupled from the atomic degrees of freedom, and the effective coupling strength between the two cavity modes scales up with

\sqrt{N}

(

N

is the number of atoms). The numerical simulation shows that the quantum swap gate still has a high fidelity under the influence of the atomic spontaneous emission and the decay of the cavity modes.

In this work we show how to engineer bilinear and quadratic Hamiltonians in cavity quantum electrodynamics through the interaction of a single driven two-level atom with cavity modes. The validity of the engineered Hamiltonians is numerically analyzed even when considering the effects of both dissipative mechanisms, the cavity field and the atom. The present scheme can be used, in both optical and microwave regimes, for quantum state preparation, the implementation of quantum logical operations, and fundamental tests of quantum theory.

In this Brief Report we present a scheme for the implementation of frequency up- and down-conversion operations in two-mode cavity quantum electrodynamics (QED). This protocol for engineering bilinear two-mode interactions could enlarge perspectives for quantum-information manipulation and also be employed for fundamental tests of quantum theory in cavity QED. As an application we show how to generate a two-mode squeezed state in cavity QED (the original entangled state of Einstein, Podolsky, and Rosen).

A single two-level atom can be used to prepare an arbitrary photon number state (Fock state) in a high Q cavity . The atom undergoes a controlled succession of interactions with two cavity modes. One of them contains a coherent field. The atom transfers photons one by one from this field to the initially empty second mode. The scheme can be extended to prepare a quantum superposition of the vacuum with a Fock state, a highly non-classical situation. We discuss the feasibility of the experiment with our present Rydberg-atom cavity QED set-up.