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Journal of Physics A Mathematical and Theoretical

Optomechanically induced anomalous population inversion in a hybrid system

Saeed Asiri, Wenchao Ge, Muhammad Suhail Zubairy

Published Apr 4, 2018• 3 citations
Publisher

Abstract

Abstract We consider a two-level atom interacting with a quantized field in an optomechanical cavity and study the population inversion of the atom in this hybrid optomechanical system. Analytical solutions of the excited state population in the hybrid system are derived for various initial states of the cavity field and the mechanical mirror in the limit of weak single-photon coupling regime. Due to the mechanical mirror, the population inversion exhibits anomalous behavior, compared to the results predicted by the Jaynes–Cummings (JC) model. For an initial Fock state cavity field, we show that the atomic population inversion can undergo collapses and revivals induced by the mechanical mirror which is in a Fock state for the resonant atom-field interaction. When the cavity field is far-detuned from the atomic transition, the atom can couple to the mechanical mirror effectively via the JC interaction. In this case, the atomic population inversion can display either full Rabi oscillations or the collapse and revival behavior induced by a Fock state or a coherent state of the mechanical mirror, respectively. We also explore an experimentally more relevant situation when the mechanical mirror is initially in a mixed state. We derive an analytical expression of the excited state population via the unitary evolution for the density operator of the whole system. We find that the population inversion in this case exhibits slower collapse and smaller revival amplitude due to the initial mixture of the mechanical state. For an initial coherent state cavity field, we show that the predicted collapse regime in the original JC model can display nonzero oscillating values. Our analytical predications are further confirmed with numerical calculations in which the dissipation mechanism from the system is included.

DOI
10.1088/1751-8121/aabb65

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Abstract We consider a two-level atom interacting with a quantized field in an optomechanical cavity and study the population inversion of the atom in this hybrid optomechanical system. Analytical solutions of the excited state population in the hybrid system are derived for various initial states of the cavity field and the mechanical mirror in the limit of weak single-photon coupling regime. Due to the mechanical mirror, the population inversion exhibits anomalous behavior, compared to the results predicted by the Jaynes–Cummings (JC) model. For an initial Fock state cavity field, we show that the atomic population inversion can undergo collapses and revivals induced by the mechanical mirror which is in a Fock state for the resonant atom-field interaction. When the cavity field is far-detuned from the atomic transition, the atom can couple to the mechanical mirror effectively via the JC interaction. In this case, the atomic population inversion can display either full Rabi oscillations or the collapse and revival behavior induced by a Fock state or a coherent state of the mechanical mirror, respectively. We also explore an experimentally more relevant situation when the mechanical mirror is initially in a mixed state. We derive an analytical expression of the excited state population via the unitary evolution for the density operator of the whole system. We find that the population inversion in this case exhibits slower collapse and smaller revival amplitude due to the initial mixture of the mechanical state. For an initial coherent state cavity field, we show that the predicted collapse regime in the original JC model can display nonzero oscillating values. Our analytical predications are further confirmed with numerical calculations in which the dissipation mechanism from the system is included.
Abstract In this paper the interaction of a three-level atom in V -configuration with a two-mode quantized field in cavity optomechanics is studied. To achieve the purpose, we first deduce the effective Hamiltonian and evaluate the explicit time-dependent form of the state vector of the whole system by choosing special initial conditions for atom, field and the oscillatory mirror. Interestingly, we can obtain the time evolution of atomic linear entropy, population inversion, quantum statistics and squeezing, both analytically and numerically. The results show that the entanglement between the atom and the subsystem of field and mirror, and all above-mentioned physical quantities can be appropriately controlled by the initial atom-field state condition, the parameters of cavity optomechanics as well as atom-field coupling strengths. In particular, the appearance of collapse-revival phenomenon in the entanglement and quantum photon statistics, also the full sub-Poissonian statistics in the two modes of field as well as in the mechanical mode of optomechanical system are noticeable features of the work.
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In this paper, we propose a new theoretical scheme for generating a macroscopic Schrödinger cat state of a mechanical oscillator in a hybrid optomechanical system where a beam of two-level atoms passes through the cavity. In the model under consideration, the cavity field couples to the macroscopic mirror through the optomechanical interaction while it couples to the atom through a generalized Jaynes–Cummings interaction that involves the cavity-mode structure. The motion of the mirror modifies the cavity-mode function and therefore modulates the atom-field interaction, leading to the three-mode atom-field-mirror coupling or, equivalently, polariton-mirror coupling in a dressed picture. This interaction induces a controllable anharmonicity in the energy spectrum of the mechanical oscillator, which provides the possibility of generating a superposition of two time-dependent coherent states of the mechanical oscillator just by performing a conditional measurement on the internal states of the atoms exiting the optomechanical cavity. We also investigate the tripartite atom-field-mirror entanglement, which is controllable by adjusting the parameters of the system. In addition, we explore the effects of the mechanical dissipation and thermal noise on the tripartite quantum correlation in the system as well as the generated mechanical superposition state.
Abstract In the photon-atom interaction, one of the most interesting phenomena can be collapse-revival effect in population inversion of atomic levels. Since a single-photon-transition Jaynes–Cummings model can be generalized to a multiphoton-transition Jaynes–Cummings model, of which the Hamiltonian can exhibit a supersymmetric Lie algebra structure, in this paper, quantum collapse and revival in atomic population inversion, which is a collaborative effect of a variety of quantum Rabi oscillations with various quantum Rabi frequencies, is studied for the supersymmetric multiphoton-transition Jaynes–Cummings model. In the literature, it has been pointed out that quantum collapse and revival might find an application in qubit design. We expect that a supersymmetric two-level system might serve as such a kind of qubits. Compared with ordinary two-level qubits, more information could be stored in the basis vectors of supersymmetric qubits, and this could increase the degrees of freedom of tensor product (multi-component extension) of basis vectors of this multiphoton-atom interacting system. For this reason, some characteristics of the collapse-revival effect driven by ordinary coherent states and Yurke–Stoler coherent states will be addressed in this paper. The influence of various characteristic parameters of this supersymmetric Jaynes–Cummings model and the quantized optical fields on the quantum collapse and revival in the population inversion will be indicated in some numerical illustrative examples.
The collapse and revival of quantum states appear in diverse areas of physics. In quantum optics the occurrence of such a phenomena in the evolution of an atomic state, interacting with a light field initially in a coherent state, was predicted by using the Jaynes-Cummings model (JCM), and subsequently demonstrated experimentally. In this paper we revisit the JCM with the Monte-Carlo wave function approach and investigate the time evolution of the photon emission rate of the atom in a cavity. Analytical and numerical quantum trajectory calculations show that the cavity and the initial field statistics strongly influence the photon emission dynamics. A coherent field indeed gives rise to a collapse and revival behavior that mirrors atomic state evolution. However, there are differences between the two. The emission rate for a field in a Fock number state exhibits a sinusoidal oscillation, and there exists a quiescent period for a thermal field. These properties are quite different from those in free space. It is also shown that the fluctuation in photon emission is much less than that of the atomic population.
Abstract In this study, we propose an experimental scheme to generate macroscopic quantum cat states of a mechanical oscillator within a hybrid atom-optomechanical system. The system consists of a mechanical oscillator harmonically coupled to an optical cavity, where the atom-cavity interaction operates in the ultrastrong-coupling regime described by the Rabi–Stark model. The cavity photon and atom state measurements project the mechanical mirror into cat states, with the process enhanced by Fock-state initialization, nonlinear atom-field coupling and modulated mechanical tuning. Wigner-function analysis confirms nonclassicality. The key findings are: (1) higher initial photon number n increases coherent-state amplitudes and separations of the cat states; (2) smaller detuning improves distinguishability; (3) both the nonlinear atom-photon coupling term and stronger optomechanical coupling accelerate the generation of cat states. This approach provides a parameter-tunable framework for quantum coherence control.