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arXiv:1503.08403 · Journal of Physics B Atomic Molecular and Optical Physics

Amplitude modulated Bloch oscillations of photon probability distribution in a cavity–atom system

G Zhang, WH Hu, Z Song

Published Mar 17, 2015• 2 citations
arXivHTMLPDF

Abstract

We study the dynamics of the Rabi Hamiltonian in the medium coupling regime with | g / ω | ∼ 0.07 , where g is the atom-field coupling constant and ω is the field frequency, for the quantum state with average photon number n ¯ ∼ 10 4 . We map the original Hamiltonian to an effective one, which describes a tight-binding chain subjected to a staggered linear potential. It is shown that the photon probability distribution of a Gaussian-type state exhibits amplitude-modulated Bloch oscillations (BOs), which are a superposition of two conventional BOs with a half-BO-period delay between them and are essentially another type of Bloch–Zener oscillation. The probability transition between the two BOs can be controlled and suppressed by the ratio g n ¯ / ω , as well as the in-phase resonant oscillating atomic frequency Ω ( t ), leading to multiple zero-transition points.

DOI
10.1088/0953-4075/48/7/075402

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We study the dynamics of the Rabi Hamiltonian in the medium coupling regime with | g / ω | ∼ 0.07 , where g is the atom-field coupling constant and ω is the field frequency, for the quantum state with average photon number n ¯ ∼ 10 4 . We map the original Hamiltonian to an effective one, which describes a tight-binding chain subjected to a staggered linear potential. It is shown that the photon probability distribution of a Gaussian-type state exhibits amplitude-modulated Bloch oscillations (BOs), which are a superposition of two conventional BOs with a half-BO-period delay between them and are essentially another type of Bloch–Zener oscillation. The probability transition between the two BOs can be controlled and suppressed by the ratio g n ¯ / ω , as well as the in-phase resonant oscillating atomic frequency Ω ( t ), leading to multiple zero-transition points.
We present a model of one-dimensional chain of two-level artificial atoms driven with DC field and quantum light simultaneously in a strong coupling regime. The interaction of atoms with light leads to electron-photon entanglement (dressing of the atoms with light). The driving via dc field leads to the Bloch oscillations (BO) in the chain of dressed atoms. We consider the mutual influence of dressing and BO and show that scenario of oscillations dramatically differs from predicted by the Jaynes-Cummings and Bloch-Zener models. We study the evolution of the population inversion, tunneling current, photon probability distribution, mean number of photons, and photon number variance, and show the influence of BO on the quantum-statistical characteristics of light. For example, the collapse-revivals picture and vacuum Rabi-oscillations are strongly modulated with Bloch frequency. As a result, quantum properties of light and degree of electron-photon entanglement become controllable via adiabatic dc field turning. On the other hand, the low-frequency tunneling current depends on the quantum light statistics (in particular, for coherent initial state it is modulated accordingly the collapse-revivals picture). The developed model is universal with respect to the physical origin of artificial atom and frequency range of atom-light interaction. The model is adapted to the 2D-heterostructures (THz frequencies), semiconductor quantum dots (optical range), and Josephson junctions (microwaves). The data for numerical simulations are taken from recently published experiments. The obtained results open a new way in quantum state engineering and nano-photonic spectroscopy.
Abstract We study the coherent dynamics of a qubit excited by an amplitude-modulated electromagnetic field under the Rabi resonance when the frequency of the low-frequency modulation field matches the Rabi frequency in the high-frequency field. Due to the destructive interference of multiple photon processes within the ultrastrong coupling between the qubit and the low-frequency driving field, Rabi oscillations result exclusively from the Bloch–Siegert effect. It is directly observed in the time-resolved coherent dynamics as the Bloch–Siegert oscillation. In this case, triplets in the Fourier spectra of the coherent response are transformed into doublets with the splitting between the lines equal to twice the Bloch–Siegert shift. These unusual properties are demonstrated in the conditions of experiments with a nitrogen vacancy center in the diamond.
The dynamics of a charge bounded by a chain of coupled artificial atoms, interacting simultaneously with a single mode quantized electromagnetic field inside a cavity, and a constant electrostatic DC field is presented in this work. We develop an extended Jaynes-Cummings model describing this system and solve it both analytically and numerically, with good agreement between the two methods. It is shown that the charge-photon dressed state is modulated with the Bloch frequency due to the interaction with the DC field. This enables to control the quantum state of light by adiabatically changing the DC field. This novel effect might be important for the application of optical modulators, quantum computing and electrically controlled quantum antennas.
Ultracold atoms in an optical lattice Bloch oscillate when subject to a constant force. In the first work presented in this thesis we have theoretically studied the scenario where the optical lattice potential is provided by the electric field inside an optical cavity. The coherent atom-light interaction in a cavity gives rise to a backaction effect on the light field which can modify the intracavity field amplitude and phase. In our first treatment of this problem we model the cavity light field and atoms by classical fields and solve the coupled atom-light equations of motion. As a result, we find that the amplitude and phase of the transmitted light field is modulated at the Bloch frequency. Remarkably, the Bloch frequency itself is not modified by the backaction. Thus the transmitted light field can be used to observe the oscillations continuously, allowing high-precision measurement with small clouds of atoms. In the second problem presented in this thesis, we explore the band structure of the steady state solutions of the atom-cavity system. A crucial first step towards determining the band structure is the identification of an energy functional that describes the coupled atom-light system. Although, we do not include direct atom-atom interactions in our models, the coupling of the atoms to the single mode light field of the cavity introduces an effective mutual interaction which is correctly taken into account by the energy functional we introduce. Corresponding to each point in the band there exists a steady state light field associated with an average cavity photon number. The dispersive nonlinear atom-light interaction can lead to bistable solutions for this intracavity photon number. For parameters where the atom-cavity system exhibits bistability, the atomic band structure develops loop structures akin to the ones predicted for Bose-Einstein condensates in ordinary (non-cavity) optical lattices. However, in our case the nonlinearity derives from the cavity backaction rather than from direct interatomic interactions. We find both bi- and tri-stable regimes associated with the lowest band, and show that the multistability we observe can be analysed in terms of swallowtail catastrophes. Dynamic and energetic stability of the meanfield solutions is also studied, and we show that the bistable solutions have, as expected, one unstable and two stable branches. The presence of loops in the band structure can lead to a breakdown in adiabaticity during Bloch oscillations as the entire band is sampled during the dynamics. We therefore use the insight gleaned from this work in choosing parameters for the Bloch oscillation measurement proposal presented in the rest of the thesis. In the third work presented in the thesis, we go beyond the mean field description and consider effects of the quantised nature of the light and atomic fields. The cavity light field is always in contact with external electromagnetic fields through the partially transmissive mirrors. This coupling to the external modes enters as quantum noise in the dynamics of the intracavity field and can also be viewed as a manifestation of quantum measurement backaction corresponding to the continuous observation of the transmitted light field. We solve the Heisenberg-Langevin equations for linearized fluctuations about the atomic and optical meanfields and examine how this influences the signal-to-noise ratio of a measurement of external forces using this system. In particular, we investigate the effects of changing the number of atoms, the intracavity lattice depth, and the atom-light coupling strength, and show how resonances between the Bloch oscillation dynamics and the quasiparticle spectrum have a strong influence on the signal-to-noise ratio as well as heating effects. One of the hurdles we overcome along the way is the proper treatment of fluctuations about time-dependent meanfields in the context of cold atom cavity-QED.
We study the coupled translational and internal dynamics of a two-level atom in a spatially periodic optical potential created by a single-mode field in a high-finesse Fabry-Perot cavity. The strongly coupled atom-cavity system with atomic center-of-mass motion included is modeled by semiclassical nonlinear Heisenberg equations of motion with two degrees of freedom. At exact resonance between the internal atomic transition and the cavity eigenfrequency, the internal and translational degrees of freedom are separated from each other resulting in periodically modulated Rabi oscillations and regular translational motion. Near the atom-field resonance, the coupled dynamics is found to be irregular and even chaotic in the sense of extremal sensitivity to initial conditions. It is manifested as a chaotic motion of an atom in an absolutely regular spatially periodic potential in the absence of any random fluctuations. This effect may be explained as a result of the interaction of nonlinear resonances in the atom-field nonlinear pendulum whose low-frequency translational motion is modulated by the high-frequency Rabi oscillations. The irregular motion is studied in detail in numerical experiments using the arsenal of methods of the dynamical systems theory. The results obtained are compared with recent experiments with ultracold single atoms interacting with single photons in the strong-coupling regime. We estimate the ranges of the system's control parameters, the detuning, the recoil frequency, and the mean number of intracavity photons, in which the interaction of nonlinear resonances may lead, under realistic conditions, to local instability of the center-of-mass motion and some manifestations of dynamical chaos, which is the effect of interest in studying the quantum-classical correspondence and quantum chaos in atomic optics.
The interaction of a two-level atom uniformly moving along a classical trajectory with a high-Q cavity quantum mode is analyzed. The dressed-state method is used to derive a recurrence formula for the transition probability of the atom with photon emission; the temporal dynamics of this probability qualitatively depends on the Doppler shift of the atomic transition frequency, on the Rabi frequency of the atom-field system, and on the detuning of the atomic transition frequency from the field mode frequency. The emission dynamics of a moving atom is very sensitive to the detuning. Rabi-type oscillations with a frequency equal to the Doppler shift can arise under certain conditions. At resonance, the emission probability of a moving atom can considerably exceed the emission probability of an atom at rest. A plane-parallel-mirror cavity and a confocal spherical-mirror cavity are considered. It is shown that the peculiarities of Doppler-Rabi oscillations must be taken into account in micromaser theory.