P. Barberis-Blostein

From quantum feedback to probabilistic error correction: manipulation of quantum beats in cavity QED

It is shown how one can implement quantum feedback and probabilistic error correction in an open quantum system consisting of a single atom, with ground- and excited-state Zeeman structure, in a driven two-mode optical cavity. The ground-state superposition is manipulated and controlled through conditional measurements and external fields, which shield the coherence and correct quantum errors. Modeling an experimentally realistic situation demonstrates the robustness of the proposal for realization in the laboratory.

Control of conditional quantum beats in cavity QED: amplitude decoherence and phase shifts

We implement a simple feedback mechanism on a two-mode cavity QED system to preserve the Zeeman coherence of a ground state superposition that generates quantum beats on the second-order correlation function. Our investigation includes theoretical and experimental studies that show how to prevent a shift away from the Larmor frequency and associated decoherence caused by Rayleigh scattering. The protocol consists of turning off the drive of the system after the detection of a first photon and letting it evolve in the dark. Turning the drive back on after a pre-set time reveals a phase accumulated only from Larmor precession, with the amplitude of the quantum beat more than a factor of two larger than with continuous drive.

Spontaneous creation and persistence of ground-state coherence in a resonantly driven intracavity atomic ensemble

The spontaneous creation and persistence of ground-state coherence in an ensemble of intracavity Rb atoms has been observed as a quantum beat. Our system realizes a quantum eraser, where the detection of a first photon prepares a superposition of ground-state Zeeman sublevels, while detection of a second erases the stored information. Beats appear in the time-delayed photon-photon coincidence rate (intensity correlation function). We study the beats theoretically and experimentally as a function of system parameters, and find them remarkably robust against perturbations such as spontaneous emission. Although beats arise most simply through single-atom-mediated quantum interference, scattering pathways involving pairs of atoms interfere also in our intracavity experiment. We present a detailed model which identifies all sources of interference and accounts for experimental realities such as imperfect prepumping of the atomic beam, cavity birefringence, and the transit of atoms across the cavity mode.

Anomalous light shift through quantum jumps in quasiresonant Rayleigh scattering

An anomalous light shift in the precession of a ground-state Zeeman coherence is observed: the Larmor frequency increases with the strength of a drive that is blue (red) detuned from a transition out of the lower (upper) energy level. Our measurements are made on Rb 85 atoms traversing an optical cavity containing a few photons; shifts as large as 1% per photon are recorded. The anomalous shift arises from an accumulation of phase driven by quantum jumps. It is stochastic and accompanied by broadening.

Algebraic solution of the Lindblad equation for a collection of multilevel systems coupled to independent environments

We consider the Lindblad equation for a collection of multilevel systems coupled to independent environments. The equation is symmetric under the exchange of the labels associated with each system and thus the open-system dynamics takes place in the permutation-symmetric subspace of the operator space. The dimension of this space grows polynomially with the number of systems. We construct a basis of this space and a set of superoperators whose action on this basis is easily specified. For a given number of levels,

A family of many-body models which are exactly solvable analytically

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Mode-exchange collisions in an exactly solvable two-mode Bose-Einstein condensate

, these superoperators are written in terms of a bosonic realization of the generators of the Lie algebra

Field autocorrelations in electromagnetically induced transparency: Effects of a squeezed probe field

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Propagation of a probe pulse inside a Bose-Einstein condensate under conditions of electromagnetically induced transparency

. In some cases, these results enable finding an analytic solution of the master equation using known Lie-algebraic methods. To demonstrate this, we obtain an analytic expression for the state operator of a collection of three-level atoms coupled to independent radiation baths. When analytic solutions are difficult to find, the basis and the superoperators can be used to considerably reduce the computational resources required for simulations.

Effects of three-body collisions in a two-mode Bose-Einstein condensate

We present a family of many-body models which have an exact analytical solution. Surprisingly, these models include generalizations of such interesting physical systems as Bose–Einstein condensates with Josephson-type interactions. The generalization comprises the inclusion of inelastic collisions, which are present in real systems but are not accounted for in the canonical model. The unexpected insight of our paper is that the inclusion of these additional terms can render the system exactly solvable. Our results open up an arena to study many-body system properties analytically, where hitherto numerical studies had to be employed.