Rabi flopping between Bloch bands induced by a weak ac resonant field is a coherent effect involving interband transitions. Here we consider the fundamental processes of emission/absorption of quanta and Rabi oscillations in non-Hermitian two-band lattices exhibiting unbalanced non-Hermitian skin effect, and unveil an unprecedented scenario of Rabi flopping. The effective dipole moment of the transition - usually considered a bulk property - is however strongly dependent on boundary conditions, being greatly enhanced with increased Rabi frequency only when open boundaries are present. As the field strength is increased, Rabi oscillations rapidly become anharmonic, and transitions cease to be vertical in the energy-momentum plane until the system enters into an unstable regime (complex quasi-energy spectrum) due to secular amplification channels. Remaining stable even in the presence of complex energies, Rabi oscillations provide a vivid illustration of how the competition between non-Hermitian, non-local and Floquet influences can result in significant enhancements of physically measurable quantities.
The anharmonic Bloch oscillations of a light beam in the array of optical waveguides are considered. The coupling modes model (CMM) with the second order interaction is used to describe the effect analytically. The formula obtained predicts explicitly the path of the optical beam, in particular, the positions of the turning points are found. A total agreement of this formula with the numerical simulation is confirmed.
We have observed Rabi-like oscillations in a current-biased dc SQUID presenting enhanced coherence times compared to our previous realization \cite{Claudon_PRL04}. This Josephson device behaves as an anharmonic oscillator which can be driven into a coherent superposition of quantum states by resonant microwave flux pulses. Increasing the microwave amplitude, we study the evolution of the Rabi frequency from the 2-level regime to the regime of multilevel dynamics. When up to 3 levels are involved, the Rabi frequency is a clear signature of quantum behavior. At higher excitation amplitude, class…
When a two-level quantum system is irradiated with a microwave signal, in resonance with the energy difference between the levels, it starts Rabi oscillation between those states. If there are other states close, in energy, to the first two, the Rabi signal will also induce transition to those. Here, we study the probability of transition to the third state, in a three-level system, while a Rabi oscillation between the first two states is performed. We investigate the effect of pulse shaping on the probability and suggest methods for optimizing pulse shapes to reduce transition probability.
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 destructive interference of multiple photon processes at 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 Fourier spectra of the cohere…
Increasing the number of electrons in electrostatically confined quantum dots can enable faster qubit gates. Although this has been experimentally demonstrated, a detailed quantitative understanding has been missing. Here we study one- and three-electron quantum dots in silicon/silicon-germanium heterostructures within the context of electrically-driven spin resonance (EDSR) using full configuration interaction and tight binding approaches. Our calculations show that anharmonicity of the confinement potential plays an important role: while the EDSR Rabi frequency of electrons in a harmonic pot…
We propose a cavity QED approach to describe light-matter interaction between an individual anharmonic molecular vibration and an infrared cavity field. Starting from a generic Morse oscillator with quantized nuclear motion, we derive a multi-level quantum Rabi model to study vibrational polaritons beyond the rotating-wave approximation. We analyze the spectrum of vibrational polaritons in detail and compare with available experiments. For high excitation energies, the spectrum exhibits a dense manifold of true and avoided level crossings as the light-matter coupling strength and cavity freque…
We investigate the circuit quantum electrodynamics of anharmonic superconducting nanowire oscillators. The sample circuit consists of a capacitively shunted nanowire with a width of about 20 nm and a varying length up to 350 nm, capacitively coupled to an on-chip resonator. By applying microwave pulses we observe Rabi oscillations, measure coherence times and the anharmonicity of the circuit. Despite the very compact design, simple top-down fabrication and high degree of disorder in the oxidized (granular) aluminum material used, we observe lifetimes in the microsecond range.
We investigate the dynamics of a driven two-level system (classical Rabi model) using the counter-rotating-hybridized rotating wave method (CHRW), which is a simple method based on a unitary transformation with a parameter $ξ$. This approach is beyond the traditional rotating-wave approximation (Rabi-RWA) and more importantly, remains the RWA form with a renormalized tunneling strength and a modified driving strength. The reformulated rotating wave method not only possesses the same mathematical simplicity as the Rabi-RWA but also allows us to explore the effects of counter-rotating (CR) compo…
In the approach to the stationary regime, a spaser exhibits complicated and highly nonlinear dynamics with anharmonic oscillations.1 We demonstrate that these oscillations are due to Rabi oscillations of the quantum dot in the field of the nanoparticle. We show that the oscillations may or may not arise dependent on the initial conditions.
Carrier dynamics at energy level anticrossings in biased semiconductor superlattices, was studied in the time domain by solving the time-dependent Schroedinger equation. The resonant nature of interminiband Rabi oscillations has been explicitly demonstrated to arise from interference of intrawell and Bloch oscillations. We also report a simulation of direct Rabi oscillations across three minibands, in the high field regime, due to interaction between three strongly coupled minibands.
In the framework of the non-secular perturbation theory based on the Bogoliubov averaging method, the coherent dynamics of multiphoton Raman transitions in a two-level spin system driven by an amplitude-modulated microwave field is studied. Closed-form expressions for the Rabi frequencies of these transitions have been obtained beyond the rotating wave approximation for the low-frequency driving component. It is shown that spin states dressed by the high-frequency component of the driving field are shifted due to the Bloch-Siegert-like effect caused by antiresonant interactions with the strong…
We report on the strong coupling between the Bloch surface wave supported by an inorganic multilayer structure and $J$-aggregate excitons in an organic semiconductor. The dispersion curves of the resulting polariton modes are investigated by means of angle-resolved attenuated total reflection as well as photoluminescence experiments. The measured Rabi splitting is 290 meV. These results are in good agreement with those obtained from our theoretical model.
The quantum Rabi model describes the interaction between a two-level quantum system and a single bosonic mode. We propose a method to perform a quantum simulation of the quantum Rabi model introducing a novel implementation of the two-level system, provided by the occupation of Bloch bands in the first Brillouin zone by ultracold atoms in tailored optical lattices. The effective qubit interacts with a quantum harmonic oscillator implemented in an optical dipole trap. Our realistic proposal allows to experimentally investigate the quantum Rabi model for extreme parameter regimes, which are not …
We predict that a direct bandgap semiconductor (GaAs) resonantly excited by a strong ultrashort laser pulse exhibits a novel regime: kicked anharmonic Rabi oscillations (KARO). In this regime, Rabi oscillations are strongly coupled to intraband motion, and interband transitions mainly take place during short times when electrons pass near the Brillouin zone center where electron populations undergo very rapid changes. Asymmetry of the residual population distribution induces an electric current controlled by the carrier-envelope phase. The predicted effects are experimentally observable using …
Motivated by recent efforts to achieve cold fermions pairing near a Feshbach resonance, we consider the dynamics of formation of the Bardeen-Cooper-Schrieffer (BCS) state. At times shorter than the quasiparticle energy relaxation time, after the interaction is turned on, the dynamics of the system is nondissipative. We show that this collective nonlinear evolution of the BCS-Bogoliubov amplitudes (u,v) along with the pairing function, is an integrable dynamical problem, and obtain a family of exact solutions in the form of single solitons and soliton trains. We interpret the collective oscilla…
A cavity quantum electrodynamical (QED) system beyond the strong-coupling regime is expected to exhibit intriguing quantum phenomena. Here we report a direct measurement of the photon-dressed qubit transition frequencies up to four photons by harnessing the same type of state transitions in an ultrastrongly coupled circuit-QED system realized by inductively coupling a superconducting flux qubit to a coplanar-waveguide resonator. This demonstrates a convincing observation of the photon-dressed Bloch-Siegert shift in the ultrastrongly coupled quantum system. Moreover, our results show that the p…
We infer the high-frequency flux noise spectrum in a superconducting flux qubit by studying the decay of Rabi oscillations under strong driving conditions. The large anharmonicity of the qubit and its strong inductive coupling to a microwave line enabled high-amplitude driving without causing significant additional decoherence. Rabi frequencies up to 1.7 GHz were achieved, approaching the qubit's level splitting of 4.8 GHz, a regime where the rotating-wave approximation breaks down as a model for the driven dynamics. The spectral density of flux noise observed in the wide frequency range decre…
We theoretically study coherent subharmonic (multi-photon) transitions of a harmonically driven spin. We consider two cases: magnetic resonance (MR) with a misaligned, i.e., non-transversal driving field, and electrically driven spin resonance (EDSR) of an electron confined in a one-dimensional, parabolic quantum dot, subject to Rashba spin-orbit interaction. In the EDSR case, we focus on the limit where the orbital level spacing of the quantum dot is the greatest energy scale. Then, we apply time-dependent Schrieffer-Wolff erturbation theory to derive a time-dependent effective two-level Hami…
We show that the counter-rotating terms of the dispersive qubit-cavity Rabi model can produce relatively large and nonmonotonic Bloch-Siegert shifts in the cavity frequency as the system is driven through a quantum-to-classical transition. Using a weak microwave probe tone, we demonstrate experimentally this effect by monitoring the resonance frequency of a microwave cavity coupled to a transmon and driven by a microwave field with varying power. In the weakly driven regime (quantum phase), the Bloch-Siegert shift appears as a small constant frequency shift, while for strong drive (classical p…
Rabi oscillations are coherent transitions in a quantum two-level system under the influence of a resonant perturbation, with a much lower frequency dependent on the perturbation amplitude. These serve as one of the signatures of quantum coherent evolution in mesoscopic systems. It was shown recently [N. Gronbech-Jensen and M. Cirillo, Phys. Rev. Lett. 95, 067001 (2005)] that in phase qubits (current-biased Josephson junctions) this effect can be mimicked by classical oscillations arising due to the anharmonicity of the effective potential. Nevertheless, we find qualitative differences between…
Within a two-band tight binding model, we investigate the dynamics of electrons with Markoffian dephasing under the influence of static electric fields. With the help of both numerical and analytic calculations we find that the dephasing ultimately takes electrons which are initially located in one miniband to equal population of the two minibands, instead of undergoing persistent Rabi flop, as they do in the absence of scattering. Miniband localization is wholly destroyed by the intervention of dephasing. We also obtain the effective decay time for the approach to equal band populations under…
Bootstrap methods, initially developed for solving statistical and quantum field theories, have recently been shown to capture the discrete spectrum of quantum mechanical problems, such as the single particle Schrödinger equation with an anharmonic potential. The core of bootstrap methods builds on exact recursion relations of arbitrary moments of some quantum operator and the use of an adequate set of positivity criteria. We extend this methodology to models with continuous Bloch band spectra, by considering a single quantum particle in a periodic cosine potential. We find that the band struc…
On the level of single atoms and photons, the coupling between atoms and the electromagnetic field is typically very weak. By employing a cavity to confine the field, the strength of this interaction can be increased many orders of magnitude to a point where it dominates over any dissipative process. This strong-coupling regime of cavity quantum electrodynamics has been reached for real atoms in optical cavities, and for artificial atoms in circuit QED and quantum-dot systems. A signature of strong coupling is the splitting of the cavity transmission peak into a pair of resolvable peaks when a…
Semiconductor quantum dots in photonic cavities are strongly coupled light-matter systems with prospective applications in optoelectronic devices and quantum information processing. Here we present a theoretical study of the coupled exciton--light field dynamics of a planar quantum dot ensemble, treated as two-level systems, embedded in a photonic cavity modeled by Maxwell's equations. When excited by coupling an external short laser pulse into the cavity, we find an exciton-polariton-like behavior for weak excitation and Rabi oscillations for strong excitation with a sharp transition between …
We investigate the near infrared interband absorption of semiconductor quantum wells driven by intense terahertz radiation in the regime of ultrastrong coupling, where the Rabi frequency is a significant fraction of the frequency of the strongly driven transition. With the driving frequency tuned just below the lowest frequency transition between valence subbands, a particularly interesting phenomenon is observed. As the THz power increases, a new peak emerges above the frequency of the undriven exciton peak which grows and eventually becomes the larger of the two. This reversal of relative pe…
We studied the semiconductor response with respect to high intensity resonant excitation on short time scale when the contribution of the Fermi statistics of the electrons and holes prevails. We studied both the single and double pulse excitations. For the latter case we considered the time evolution of the multi-wave mixing exciton polarization. The main difference between the excitation by a single pulse or by two non-collinear pulses is that the Rabi oscillations of the multi-wave mixing response are characterized by two harmonics. Analyzing the operator dynamics governed by the external ex…
We study Rabi oscillations detected in the coherent optical response from various exciton complexes in a 20~nm-thick CdTe/(Cd,Mg)Te quantum well using time-resolved photon echoes. In order to evaluate the role of exciton localization and inhomogeneous broadening we use selective excitation with spectrally narrow ps-pulses. We demonstrate that the transient profile of the photon echo from the localized trion (X$^-$) and the donor-bound exciton (D$^0$X) transitions strongly depends on the strength of the first pulse. It acquires a non-Gaussian shape and experiences significant advancement for pu…
We discuss the coherent oscillations between two coupled quantum states of a Bose-Einstein condensate in two-dimensional space at zero temperature. In the system we consider, weak interparticle repulsive interactions occur between the particles in state one only, while the state two particles remain non-interacting. Analytical as well as numerical solution of the coupled Gross-Pitaevskii and Schroedinger equations reveals various regimes of oscillational dynamics for the relative quantum phase and population imbalance between the two subsystems of the condensate. We show that, depending on the…
We present a gauge-invariant density matrix description of non-equilibrium superconductor (SC) states with spatial and temporal correlations driven by intense terahertz (THz) lightwaves. We derive superconductor Bloch--Maxwell equations of motion that extend Anderson pseudo-spin models to include the Cooper pair center-of-mass motion and electromagnetic propagation effects. We thus describe quantum control of dynamical phases, collective modes, quasi-particle coherence, and high nonlinearities during cycles of carrier wave oscillations, which relate to our recent experiments. Coherent photogen…
We investigate second harmonic generation (SHG) from hexagonal periodic arrays of triangular nano-holes of aluminum using a self-consistent methodology based on the hydrodynamics-Maxwell-Bloch approach. It is shown that angular polarization patterns of the far-field second harmonic response abide to three-fold symmetry constraints on tensors. When a molecular layer is added to the system and its parameters are adjusted to achieve the strong coupling regime between a localized plasmon mode and molecular excitons, Rabi splitting is observed from occurrence of both single- and two-photon transiti…
