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arXiv:0711.2049 · Journal of Physics B Atomic Molecular and Optical Physics

On the role of the atom–cavity detuning in bimodal cavity experiments

Denis Gonţa, S. Fritzsche

Published Apr 23, 2008• 4 citations
arXivHTMLPDF

Abstract

The coherent evolution of the atom–cavity state in bimodal (cavity) experiments has been analysed for a realistic time dependence in detuning the atomic transition frequency. Apart from a 'smooth switch' of the atomic resonance from one to the second mode of a bimodal cavity, we considered also an additional (effective) interaction between the field modes of the cavity, known as a 'communication channel'. Comparison of our model computations has been made especially with the measurements by Rauschenbeutel et al (2001 Phys. Rev. A 64 050301) who demonstrated for the first time the entanglement of the field modes in a bimodal cavity. It is shown that the agreement between the (theoretically) predicted and experimental phase shifts can be improved by allowing a 'communication' between the two field modes during a short but finite switch of the atomic transition frequency from one mode to the other. We therefore suggest that the details of the atom–cavity detuning should be taken into account for the future interpretation of bimodal cavity experiments.

DOI
10.1088/0953-4075/41/9/095503

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The coherent evolution of the atom–cavity state in bimodal (cavity) experiments has been analysed for a realistic time dependence in detuning the atomic transition frequency. Apart from a 'smooth switch' of the atomic resonance from one to the second mode of a bimodal cavity, we considered also an additional (effective) interaction between the field modes of the cavity, known as a 'communication channel'. Comparison of our model computations has been made especially with the measurements by Rauschenbeutel et al (2001 Phys. Rev. A 64 050301) who demonstrated for the first time the entanglement of the field modes in a bimodal cavity. It is shown that the agreement between the (theoretically) predicted and experimental phase shifts can be improved by allowing a 'communication' between the two field modes during a short but finite switch of the atomic transition frequency from one mode to the other. We therefore suggest that the details of the atom–cavity detuning should be taken into account for the future interpretation of bimodal cavity experiments.
The authors calculate the asymptotic quantum state of a driven cavity mode interacting with a two-state atom when the dipole coupling constant is much larger than the atomic and cavity linewidths. They show that a novel symmetry breaking transition occurs as the strength of the driving field is increased. Although the driving field, the cavity mode, and the atom are all resonant, above the transition threshold the intracavity field shows a bimodality in phase. The bimodality results from an intensity-dependent detuning between the driving field and the transition frequencies of the composite atom-cavity-mode 'molecule.' Well above the transition threshold the driven cavity mode plus atom behaves as a driven harmonic oscillator with randomly switched detuning; the detuning (and hence the phase of the interactivity field) changes sign each time the atom makes a spontaneous transition between dressed states.
A new conditional scheme for entangling the two quantized modes of a bimodal high-Q cavity field is presented. We show that, injecting one at time k atoms inside the cavity, it is possible to guide the field toward k-dependent linear combinations of k + 1 bimodal Fock states, each one possessing the same total number of photons. The two simple cases corresponding to the passage of one or two atoms only through the resonator are considered. Their practical feasibility against cavity losses, spontaneous emission and other sources of imprecision of the experimental set-up is discussed. Two examples illustrating the usefulness of and the interest toward the creation of such a local entanglement, are reported. The first one relates the specific features of these bimodal entangled states to the occurrence of a non-classical correlation effect in the dynamics of a two-level atom interacting with the entangled cavity. The second one demonstrates that the peculiar entanglement initially stored in the cavity in accordance with our method, provides an effectively exploitable resource to entangle two spatially separated cavities.
We show a procedure for engineering effective interactions between two modes in a bimodal cavity. Our system consists of one or more two-level atoms, excited by a classical field, interacting with both modes. The two effective Hamiltonians have forms similar to beam-splitter and quadratic beam-splitter interactions. We also demonstrate that the nonlinear Hamiltonian can be used to prepare an entangled coherent state, also known as a multidimensional entangled coherent state, which has been pointed out as an important entanglement resource. We show that the nonlinear interaction parameter can be enhanced considering NNN independent atoms trapped inside a high-finesse optical cavity.
Considering the adiabatical approximation and the large detuning condition, we give the effective Hamiltonian of a ladder-type three levels atom interacting with a bimodal cavity field. If two identical three-level atoms are sent through the cavity one by one, a two-atom entangled state can be generated. With the choice of the appropriate interaction time, a maximally entangled state of two atoms can be obtained if decoherence effect is ignored. Moreover, we discuss the effect of cavity decay on four physical quantities including atomic population probability, residual entanglement of the first atom and the cavity field, concurrence between the two atoms, and fidelity for generating atomic EPR state, all of which decrease with the increase of cavity decay when the other parameters are fixed.
We measure the transmission spectrum of an optical cavity filled with two-level atoms. For small intensities, the coupling between atoms and a single mode of the cavity splits the spectrum into two normal modes: the vacuum Rabi peaks. We gradually decouple the system in two ways and study the evolution of the vacuum Rabi peaks. First we lower the atom-cavity coupling frequency through its intensity dependence, showing that the peaks shift, deform, exhibit frequency hysteresis, and eventually merge into a single peak that approaches the empty cavity resonance. Second we detune the atoms and the cavity mode and observe an avoided crossing. The normal modes of the coupled system transform into the two resonances of the uncoupled system. We map out the transition region and find good agreement with theoretical predictions.
It has been recently shown [1] that, under suitable conditions, the interaction between a three-level atom and the quantized field of a bimodal microcavity may be effectively reduced to the two-photon coupling between a single two-level atom and the electromagnetic field in the resonator. The corresponding Hamiltonian model is characterized by intensity-dependent Stark shifts due to the presence of an intermediate off-resonance atomic level. Assume the cavity field prepared at in an arbitrary state and let an initially excited atom cross the cavity with an appropriately selected velocity. It is possible to show that, exploiting a single conditional measurement of the atomic state immediately after the atom leaves the resonator, the bimodal field is projected into a new state characterized by the same photon number distribution present at More in detail, the experimental scheme we propose makes it possible manipulating only the phases of the initial probability amplitudes of finding a well defined population in the cavity. We prove that the state into which the cavity collapses after a successful atomic measurement is unitarily related to the initial field state and the explicit form of the accomplishing operator is constructed. We wish to remark that, beside its inherent theoretical interest, this simple experimental scheme might also be of relevance in the socalled field of quantum communication [2], where implementing unitary modifications of a quantum state signal represents an issue of topical and central importance. More in general, our proposal provides a systematic procedure for controlling selected properties of a quantum state. We in fact demonstrate that our experimental scheme may be reliably exploited to generate orthogonal states to a prefixed one or to control the squeezing direction.