Atom-field Dynamics Research Articles

Atom-field dynamics in curved spacetime

Atom-field dynamics in curved spacetime

Pulsed field transmission by atomic frequency combs and random spike media: The prominent role of dispersion

A theory of pulse transmission is presented in which the medium through which the pulse propagates is characterized by an inhomogeneous distribution that is either an atomic frequency comb (AFC) or a medium of randomly spaced frequency spikes (RSM). For an AFC, we obtain analytic expressions for the transmitted field amplitude, which is composed of the (partially) transmitted incident pulse, plus a train of equally spaced echoes. For RSM, we derive expressions for the average transmitted field amplitude and field intensity. In the limit that the spike width is much less than the spike separation, normally encountered with AFC, the overall atom-field dynamics is dominated by dispersion---absorption plays a negligible role. The importance of the average group time delay of the pulse is discussed.

Optomechanical cooling and self-trapping of low field seeking point-like particles

Atoms in spatially dependent light fields are attracted to local intensity maxima or minima depending on the sign of the frequency difference between the light and the atomic resonance. For light fields confined in open high-Q optical resonators the backaction of the atoms onto the light field generates dissipative dynamic opto-mechanical potentials, which can be used to cool and trap the atoms. Extending the conventional case of high field seekers to the regime of blue atom-field detuning, where the particles are low field seeking, we show that inherent nonlinear atom field dynamics still can be tailored to cool and trap near zero field intensity. Studying field intensity, particle localization and kinetic energy for cavity driving or pumping the particle from the side, we identify optimal parameter regimes, where sub-Doppler cooling comes with trapping and minimal atomic saturation.

Mixed Rabi Jaynes–Cummings model of a three-level atom interacting with two quantized fields

The quantum Rabi model describes the ultrastrong interaction of a two-level atom coupled to a single quantized bosonic mode. As compared to the Jaynes–Cummings model, in the Rabi model the absorption and emission processes do not need to satisfy energy conservation and the usual rotating wave approximation (RWA) breaks down. As a result, the atom-field dynamics in the Hilbert space splits into two independent parity chains, exhibiting a collapse-revival pattern and exact periodic dynamics in the limit of degenerate atomic levels. Here we introduce a mixed Rabi Jaynes–Cummings model by considering a three-level atom interacting with two quantized bosonic fields, in which the RWA is made for one transition (with a weak atom-field coupling) but not for the other one (with an ultrastrong atom-field coupling). As a result, we show that the field in the weak coupled atomic transition can be used as a tool to control the atom-field dynamics of the other (strong coupled) transition, thus realizing an effective two-level quantum Rabi model with a controllable field. In particular, a periodic temporal dynamics of the atom-field state can be realized by appropriate tuning of the weak control field, even for non-degenerate atomic levels. A photonic simulator of the mixed Rabi Jaynes–Cummings model, based on light transport in evanescently coupled optical waveguide lattices, is also briefly discussed.

Frequency response of an atomic resonance driven by weak free-electron-laser fluctuating pulses

Motivated by recent experiments pertaining to the interaction of weak SASE-free-electron-laser (FEL) pulses with atoms and molecules, we investigate the conditions under which such interactions can be described in the framework of a simple phase-diffusion model with decorrelated atom–field dynamics. The nature of the fluctuations that are inevitably present in SASE-FEL pulses is shown to play a pivotal role in the success of the decorrelation. Our analysis is performed in connection with specific recent experimental results from FLASH in the soft x-ray regime.

The effect of frequency-mismatched spontaneous emission on atom-field entanglement

A Schrödinger representation approach is used to calculate the atom-field dynamics following spontaneous emission by an atom in its excited state to a superposition of its two ground-state sublevels, in the case where the frequency separation of the ground-state sublevels is large compared to the excited-state decay rate. The emitted radiation is incident on a broadband photodetector. Using a relatively simple model for the photodetector, we show how a measurement of a photo-signal leaves the atom in a coherent superposition of the two ground states. The relative phase between the two ground-state amplitudes can be interpreted in terms of the temporal phase acquired in the time interval between spontaneous emission (viewed as a quantum jump process) and detection. Alternatively, the phase can be associated with a spatial phase of the entangled atom-field system; the source atom is projected into a state containing this spatial phase when the emitted photon is detected.

Optical realization of the atom–field interaction in waveguide lattices

A classical realization of the atom–field interaction Hamiltonian, based on the transport of light in engineered optical waveguide lattices, is theoretically proposed. The optical lattice enables direct visualization of atom–field dynamics in Fock space.

Analytical and numerical analysis of the atom–field dynamics in non-stationary cavity QED

We study analytically and numerically the dynamics of the quantum non-stationary system composed of a two-level atom interacting with a single mode cavity field whose frequency is rapidly modulated in time (with a small amplitude). We identify modulation laws resulting in qualitatively different dynamical regimes and we present analytical solutions in some simple cases. In particular, we analyse minutely the influence of the field–atom coupling on the photon generation from vacuum via the dynamical Casimir effect.

Nonlinear atom-field dynamics in high-Q cavities: from a BEC to a thermal gas

A cold gas of polarizable particles moving in the optical potential of a standing wave high finesse optical resonator acts as a dynamic refractive index. For a sufficiently strong cavity pump the optical forces generated by the intra cavity field perturb the particles phase space distribution, which shifts the optical resonance frequency and induces a nonlinear optical response. By help of the corresponding Vlasov equation we predict that beyond the known phenomenon of optical bi-stability one finds regions in parameter space, where no stable stationary solution exists. The atom field dynamics then exhibits oscillatory solutions converging to stable limit cycles of the system. The linearized analytical predictions agree well with corresponding numerical solutions of the full time dependent equations and first experimental observation in both cases.

Absorption of a pulse by an optically dense medium: An argument for field quantization

The theory of the absorption of a weak optical pulse by an optically dense medium is shown to lead to unphysical results unless the radiation field is quantized. In contrast to the photoelectric effect, the atom-field dynamics for pulsed field absorption can be obtained using elementary quantum mechanics without imposing any assumptions on the nature of the detection process. As such, pulsed field absorption offers distinct advantages over the photoelectric effect as a proving ground for field quantization. If the classical field pulse is replaced by a quantized, multimode field state, many classical field results are recovered without the inconsistencies that arise in the classical field calculation.

Resonant atom-field interaction in large-size coupled-cavity arrays

We consider an array of coupled cavities with staggered intercavity couplings, where each cavity mode interacts with an atom. In contrast to large-size arrays with uniform hopping rates where the atomic dynamics is known to be frozen in the strong-hopping regime, we show that resonant atom-field dynamics with significant energy exchange can occur in the case of staggered hopping rates even in the thermodynamic limit. This effect arises from the joint emergence of an energy gap in the free photonic dispersion relation and a discrete frequency at the gap's center. The latter corresponds to a bound normal mode stemming solely from the finiteness of the array length. Depending on which cavity is excited, either the atomic dynamics is frozen or a Jaynes-Cummings-like energy exchange is triggered between the bound photonic mode and its atomic analog. As these phenomena are effective with any number of cavities, they are prone to be experimentally observed even in small-size arrays.

Semiclassical dynamics from Zeno-like measurements

The usual semiclassical approximation for atom–field dynamics consists in substituting the field operators by complex numbers related to the (supposedly large enough) intensity of the field. We show that a semiclassical evolution for coupled systems can always be obtained by frequent Zeno-like measurements on the state of one subsystems, independently of the field intensity in the example given. We study the Jaynes–Cummings model from this perspective.

Nonequilibrium thermal Casimir–Polder forces

We study the nonequilibrium Casimir–Polder force on an atom prepared in an incoherent superposition of internal energy eigenstates, which is placed in a magnetoelectric environment of nonuniform temperature. After solving the coupled atom–field dynamics within the framework of macroscopic quantum electrodynamics, we derive a general expression for the thermal Casimir–Polder force.

Collapse and revival of the Doppler-Rabi oscillations of a moving atom in a cavity

Collapse and revival of the Doppler-Rabi oscillations of a two-level atom moving in a cavity electromagnetic field are analyzed. The coupled atom-field dynamics are predicted accurately by numerical calculation and approximately by using the stationary phase approximation combined with the Poisson summation formula. The collapse and revival patterns are shown to be qualitatively different in the cases of moving atom and atom at rest. In particular, quantum revivals of Doppler-Rabi oscillations occur with a period determined by the Doppler shift of the atomic transition frequency. This regime of Doppler-Rabi oscillations requires that the Rabi frequency and the Doppler shift satisfy the condition ΩR ≪ ΩD. Under the inverse relation, the collapse- revival phenomenon generally does not occur. It is shown that even a small amount of atom-cavity detuning eliminates collapse-revival behavior. The analysis is performed for both coherent and thermal cavity fields.

Ultra-cold atoms in an optical cavity: two-mode laser locking to the cavity avoiding radiation pressure

The combination of ultra-cold atomic clouds with the light fields of optical cavities provides a powerful model system for the development of new types of laser cooling and for studying cooperative phenomena. These experiments critically depend on the precise tuning of an incident pump laser with respect to a cavity resonance. Here, we present a simple and reliable experimental tuning scheme based on a two-mode laser spectrometer. The scheme uses a first laser for probing higher-order transversal modes of the cavity having an intensity minimum near the cavity’s optical axis, where the atoms are confined by a magnetic trap. In this way the cavity resonance is observed without exposing the atoms to unwanted radiation pressure. A second laser, which is phase locked to the first and tuned close to a fundamental cavity mode, drives the coherent atom-field dynamics.

Theory of a single-atom laser including light forces

We study a single incoherently pumped atom moving within an optical high-$Q$ resonator in the strong-coupling regime. Using a semiclassical description for the atom and field dynamics, we derive a closed system of differential equations to describe this coupled atom-field dynamics. For sufficiently strong pumping, the system starts lasing when the atom gets close to a field antinode, and the associated light forces provide for self-trapping of the atom. For a cavity mode blue detuned with respect to the atomic transition frequency, this is combined with cavity-induced motional cooling, allowing for long-term steady-state operation of such a laser. The analytical results for temperature and field statistics agree well with our earlier predictions based on quantum Monte Carlo simulations. We find sub-Doppler temperatures that decrease with gain and coupling strength, and can even go beyond the limit of passive cavity cooling. Besides demonstrating the importance of light forces in single-atom lasers, this result also gives strong evidence to enhance laser cooling through stimulated emission in resonators.

Quantum motion of laser-driven atoms in a cavity field

We investigate the quantum motion of coherently driven ultracold atoms in the field of a damped high-Q optical cavity mode. The laser field is chosen far detuned from the atomic transition but close to a cavity resonance, so that spontaneous emission is strongly suppressed but a coherent field builds up in the resonator by stimulated scattering. On one hand the shape of the atomic wave function determines the field dynamics via the magnitude of the scattering and the effective refractive index the atoms create for the mode. The mode intensity on the other hand determines the optical dipole force on the atoms. The system shows rich coupled atom-field dynamics including self-organisation, self trapping, cooling or heating. In the limit of deep trapping we are able to derive a system of closed, coupled equations for a finite set of atomic expectations values and the field. This allows to determine the self consistent ground state of the system as well as the eigenfrequencies and damping rates for excitations.

Atomic self-trapping induced by single-atom lasing.

We study atomic center of mass motion and field dynamics of a single-atom laser consisting of a single incoherently pumped free atom moving in an optical high-Q resonator. For sufficient pumping, the system starts lasing whenever the atom is close to a field antinode. If the field mode eigenfrequency is larger than the atomic transition frequency, the generated laser light attracts the atom to the field antinode and cools its motion. Using quantum Monte Carlo wave function simulations, we investigate this coupled atom-field dynamics including photon recoil and cavity decay. In the regime of strong coupling, the generated field shows strong nonclassical features such as photon antibunching, and the atom is spatially confined and cooled to sub-Doppler temperatures.

A quantum stochastic approach to the spectrum of a two-level atom

By means of quantum stochastic calculus we construct a model for an atom with two degenerate levels and stimulated by a laser and we compute its fluorescence spectrum; let us stress that, once the model for the unitary atom-field dynamics has been given, then the spectrum is computed without further approximations. If only the absorption/emission term is included in the interaction, we reobtain the Mollow spectrum in the case of a monochromatic laser and the Kimble-Mandel spectrum in the case of a "phase diffusion model" for a non monochromatic laser. However, our model can describe also another type of light scattering, a "direct scattering" due to the response of the atom as a whole, which we expect to be small, but which interferes with the scattering due to the absorption/emission channel. When both the scattering channels are introduced we obtain a modification of the Mollow-Kimble-Mandel spectrum, which shares the main features with the usual case, but which presents some asymmetries even in the case of no detuning.

Trapping States in the Micromaser

Trapping states in the one-atom maser or micromaser are predicted by maser theory and are a direct consequence of the quantization of the electromagnetic field. They have been found in our experiment when the inversion of atoms leaving the cavity is observed while the interaction time is scanned. They correspond to quantum states of the atom-cavity system and under certain conditions represent Fock states. The trapping states occur when the atom-field dynamics complete a full evolution (or multiples thereof). Owing to feedback through the maser dynamics, a stabilization of the photon number in the steady state field of the maser cavity is achieved.