Jonas Larson

Dynamics of the Jaynes–Cummings and Rabi models: old wine in new bottles

By using a wavepacket approach, this paper reviews the Jaynes–Cummings model with and without the rotating wave approximation (RWA) in a non-standard way. This gives new insight, not only of the two models themselves, but of the RWA as well. Expressing the models by field quadrature operators, instead of the typically used boson ladder operators, wavepacket simulations are presented. Several known phenomena of these systems, such as collapse-revivals, Rabi oscillation, squeezing and entanglement, are reviewed and explained in this new picture, either in an adiabatic or diabatic frame. The harmonic shape of the potential curves that the wavepackets evolve on and the existence of a level crossing make these results interesting in a broader sense not only for models in quantum optics, but especially in atomic and molecular physics.

Cavity-state preparation using adiabatic transfer

We show how to prepare a variety of cavity field states for multiple cavities. The state preparation technique used is related to the method of stimulated adiabatic Raman passage. The cavity modes are coupled by atoms, making it possible to transfer an arbitrary cavity field state from one cavity to another and also to prepare nontrivial cavity field states. In particular, we show how to prepare entangled states of two or more cavities, such as an Einstein-Podolsky-Rosen state and a W state, as well as various entangled superpositions of coherent states in different cavities, including Schrodinger cat states. The theoretical considerations are supported by numerical simulations.

Validity of adiabaticity in cavity QED

This paper deals with the concept of adiabaticity for fully quantum mechanical cavity QED models. The physically interesting cases of Gaussian and standing wave shapes of the cavity mode are considered. An analytical approximate measure for adiabaticity is given and compared with numerical wave packet simulations. Good agreement is obtained where the approximations are expected to be valid. Usually for cavity QED systems, the large atom-field detuning case is considered as the adiabatic limit. We, however, show that adiabaticity is also valid, for the Gaussian mode shape, in the opposite limit. Effective semiclassical time-dependent models, which do not take into account the shape of the wave packet, are derived. Corrections to such an effective theory, which are purely quantum mechanical, are discussed. It is shown that many of the results presented can be applied to time-dependent two-level systems.

Dynamics of a Raman coupled model: entanglement and quantum computation

The evolution of a Raman coupled three-level Lambda atom with two quantized cavity modes is studied in the large detuning case; i.e. when the upper atomic level can be adiabatically eliminated. Par ...

On the rotating wave approximation in the adiabatic limit

I revisit a longstanding question in quantum optics; when is the rotating wave approximation justified? In terms of the Jaynes–Cummings and Rabi models I demonstrate that the approximation in general breaks down in the adiabatic limit regardless of system parameters. This is explicitly shown by comparing Berry phases of the two models, where it is found that this geometrical phase is strictly zero in the Rabi model contrary to the non-trivial Berry phase of the Jaynes–Cummings model. The source of this surprising result is traced back to different topologies in the two models.

Effective mass in cavity QED

We consider propagation of a two-level atom coupled to one electromagnetic mode of a high-Q cavity. The atomic center-of-mass motion is treated quantum mechanically and we use a standing wave shape for the mode. The periodicity of the Hamiltonian leads to a spectrum consisting of bands and gaps, which is studied from a Floquet point of view. Based on the band theory, we introduce a set of effective mass parameters that approximately describe the effect of the cavity on the atomic motion, with the emphasis on one associated with the group velocity and on another one that coincides with the conventional effective mass. Propagation of initially Gaussian wave packets is also studied using numerical simulations and the mass parameters extracted thereof are compared with those predicted by the Floquet theory. Scattering and transmission of the wave packet against the cavity are further analyzed, and the constraints for the effective mass approach to be valid are discussed in detail.

Adiabatic state preparation in a cavity

The paper discusses the single-mode Jaynes-Cummings model with time-dependent parameters. Solvable models for two-level systems are utilized to consider the changes in the photon distribution effected by the passage of atoms through the cavity. It is suggested that such systems may be used as filters to modify the photon distribution. The effect can be enhanced by repeatedly sending new atoms through the cavity. We show that such filters can cut out either small or large photon numbers. It is also shown that the method can be used to narrow down photon distributions and in this way achieve highly non-classical sub-Poissonian states. Some limitations and applications of the method are presented.

Scheme for generating entangled states of two field modes in a cavity

This paper considers a two-level atom interacting with two cavity modes with equal frequencies. Applying a unitary transformation, the system reduces to the analytically solvable Jaynes–Cummings model. For some particular field states, coherent and squeezed states, the transformation between the two bare bases, related by the unitary transformation, becomes particularly simple. It is shown how to generate (the highly non-classical) entangled coherent states of the two modes, both in the zero and large detuning cases. An advantage of the zero detuning case is that the preparation is deterministic and no atomic measurement is needed. For the large detuning situation, a measurement is required, leaving the field in either of two orthogonal entangled coherent states.

Loading of bosons in optical lattices into the p band

We present a method for transferring bosonic atoms residing on the lowest s band of an optical lattice to the first excited p bands. Our idea hinges on resonant tunneling between adjacent sites of accelerated lattices. The acceleration effectively shifts the quasibound energies on each site such that the system can be cast into a Wannier-Stark ladder problem. By adjusting the acceleration constant, a situation of resonant tunneling between the s and p bands is achievable. Within a mean-field model, considering {sup 87}Rb atoms, we demonstrate population transfer from the s to the p bands with around 95% efficiency. Nonlinear effects deriving from atom-atom interactions, as well as coupling of the quasibound Wannier-Stark states to the energy continuum, are considered.

Rabi oscillations in a quantum dot-cavity system coupled to a nonzero temperature phonon bath

We study a quantum dot strongly coupled to a single high-finesse optical microcavity mode. We use a rotating wave approximation (RWA) method, commonly used in ion–laser interactions, together with the Lamb–Dicke approximation to obtain an analytic solution of this problem. The decay of Rabi oscillations because of the electron–phonon coupling is studied at arbitrary temperature and analytical expressions for the collapse and revival times are presented. Analyses without the RWA are presented as means of investigating the energy spectrum.