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Cavity QED with Center of Mass Tunneling

Charles H. Baldwin

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

We model the evolution of a single atom in a cavity interacting with two lasers, one far off resonance which creates an optical potential lattice and one near resonance, which can interact with the atom.The atom may tunnel between sites in the lattice.We find that the photon counting statistic g (2) (τ ) depends on the tunneling rate.Additionally we derive methods to work with a Bose-Einstein Condensate in the same situation.It is shown that oscillations in g (2) (τ ) are directly proportional to the tunneling coefficient given in our models.

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We model the evolution of a single atom in a cavity interacting with two lasers, one far off resonance which creates an optical potential lattice and one near resonance, which can interact with the atom.The atom may tunnel between sites in the lattice.We find that the photon counting statistic g (2) (τ ) depends on the tunneling rate.Additionally we derive methods to work with a Bose-Einstein Condensate in the same situation.It is shown that oscillations in g (2) (τ ) are directly proportional to the tunneling coefficient given in our models.
We model the evolution of a single atom in a cavity interacting with two lasers, one far off resonance which creates an optical potential lattice and one near resonance, which can interact with the atom. The atom may tunnel between sites in the lattice. We find the photon counting statistic g(2)(τ)g^{(2)}(τ)g(2)(τ) depends on the tunneling rate. Additionally we derive methods to work with a Bose-Einstein Condensate in the same situation, in ther Josephson junction regime. It is shown that oscillations in g(2)(τ)g^{(2)}(τ)g(2)(τ) are directly proportional to the tunneling coefficient. We work in the bad-cavity limit and give an example of the use of adiabatic elimination in quantum trajectory theory
We present a theoretical treatment of dynamics of an atomic Bose-Einstein condensation interacting witha single-mode quantized travelling-wave laser field in a double-well potential. When the atom-field system is initiallyin a coherent state, expressions for the energy exchange between atoms and photons are derived. It is revealed thatatoms in the two wells can be in a self-trapping state when the tunnelling frequency satisfies two specific conditions,in which the resonant and far off-resonant cases are included. It is found that there is an alternating current with twodifferent sinusoidal oscillations between the two wells, but no dc characteristic of the atomic tunnelling current occurs.It should be emphasized that when without the laser field, both the population difference and the atomic tunnellingcurrent are only a single oscillation. But they will respectively become a superposition of two oscillations with differentoscillatory frequencies in the presence of the laser field. For the two oscillations of the population difference, one alwayshas an increment in the oscillatory frequency, the other can have an increment or a decrease under different cases. Theseconclusions are also suitable to those of the atomic tunnelling current. As a possible application, by measurement of theatomic tunnelling current between the two wells, the number of Bose-condensed atoms can be evaluated. lBy properlyselecting the laser field, the expected atomic tunnelling current can be obtained too.
We present a theoretical treatment of dynamics of an atomic Bose–Einstein condensation interacting with a single-mode quantized travelling-wave laser field in a double-well potential. When the atom-field system is initially in a coherent state, expressions for the energy exchange between atoms and photons are derived. It is revealed that atoms in the two wells can be in a self-trapping state when the tunnelling frequency satisfies two specific conditions, in which the resonant and far off-resonant cases are included. It is found that there is an alternating current with two different sinusoidal oscillations between the two wells, but no dc characteristic of the atomic tunnelling current occurs. It should be emphasized that when without the laser field, both the population difference and the atomic tunnelling current are only a single oscillation. But they will respectively become a superposition of two oscillations with different oscillatory frequencies in the presence of the laser field. For the two oscillations of the population difference, one always has an increment in the oscillatory frequency, the other can have an increment or a decrease under different cases. These conclusions are also suitable to those of the atomic tunnelling current. As a possible application, by measurement of the atomic tunnelling current between the two wells, the number of Bose-condensed atoms can be evaluated. By properly selecting the laser field, the expected atomic tunnelling current can be obtained too.
We investigate the interplay dynamics of a cavity QED system, where the two-level atoms are trapped in a double-well potential, and the cavity mode, with a frequency largely detuned from the atomic level splitting, is driven by a probe laser. The interaction between the center-of-mass motion of the atoms and the cavity mode is induced by the position-dependent atom-field coupling. The dynamics of the system is characterized by two distinct time scales, the inverse of the atomic interwell tunneling rate and the inverse of the cavity loss rate. The system shows drastically different (quasi)steady behaviors in the short- and long-time intervals, and the detection of the statistics of atom number distribution from the transmission spectra is available only in the short-time interval.
In this work, we will look at the dynamics of a two-level atom in a damped, driven optical cavity in which atomic center-of-mass motion (CMM) is quantized.Of particular interest is the addition of an external potential (not related to the cavity field) in the cavity that effects the atom.Specifically, we are introducing to the system Hamiltonian a harmonic potential that effectively represents the presence of an optical lattice within the cavity.Thus, we are interested in the interplay of cold atoms and cavity QED.The form of our investigation of the system's dynamics will be in the study of the photon statistics and field-intensity correlation of the transmitted and fluoresced fields.
A Bose–Einstein condensate is dispersively coupled to a single mode of an ultra-high finesse optical cavity. The system is governed by strong interactions between the atomic motion and the light field even at the level of single quanta. While coherently pumping the cavity mode the condensate is subject to the cavity optical lattice potential whose depth depends nonlinearly on the atomic density distribution. We observe optical bistability already below the single photon level and strong back-action dynamics which tunes the coupled system periodically out of resonance.