We investigate laser-driven vibronic transitions of a single two-level atomic ion in harmonic and hard wall traps. In the Lamb-Dicke regime, for tuned or detuned lasers with respect to the internal frequency of the ion, and weak or strong laser intensities, the vibronic transitions occur at well isolated "Rabi Resonances", where the detuning-adapted Rabi frequency coincides with the level spacing of the vibrational modes. These vibronic resonances are characterized as avoided crossings of the dressed levels (eigenvalues of the full Hamiltonian). Their peculiarities due to symmetry constraints and trapping potential are also examined.
Vibronic coupling effects usually manifest themselves in molecules and crystals rather than in an unbound atoms. We theoretically demonstrate the existence of vibronic states in a moving two-level atom exposed to a strong electromagnetic wave. In this case, the Rabi oscillations of the electron density give rise to periodic displacements of the atom center of mass with the Rabi frequency. The periodic displacements mix the Stark split electron levels and lead to the establishment of a channel for energy transfer in the photon-electron-center-of-mass system. Such a channel paves the way for fas…
The interacting model describing the Rabi transition is essential in studying atom-photon interactions, where the kinetic energy term is often neglected for the convenience of analysis. We first study the approximation through the fidelity approach and verify its valid region in the parameter space of detuning and momentum. We find that as the radiation field's momentum and the absolute value of detuning decrease, the approximation becomes valid. We further discover that the omission of the kinetic energy term will overestimate the measuring accuracy of the Rabi frequency in some parameter reg…
We studied full revivals of quantum states in the Jaynes-Cannings model. It is proved that in the case of zero detuning in subspaces generated by two adjacent pairs of energy levels, full revival of the subspace does not exist for any values of the parameters. In the case of non-zero detuning on the contrary, the set of parameters that allows full revival of such subspaces is dense as the subset of all parameters. The nature of these revivals differs from Rabi oscillations in subspaces of a single pair of energy. In more complex subspaces the presence of full revival is reduced to particular c…
QED-model for multichain coupled qubit system, proposed in \cite{Part1}, was confirmed by Raman scattering studies of carbon zigzag-shaped nanotubes, produced by high energy ion beam modification of natural diamond single crystals. New quantum optics phenomenon - Rabi waves - has been experimentally identified for the first time. Raman spectra in perfect quasi-1D carbon nanotubes are quite different in comparison with well known Raman spectra in 2D carbon nanotubes of larger diameter. They characterized by vibronic mode of Su-Schriffer-Heeger $σ$-polaron lattice and its revival part in frequen…
The dynamics of a vibronic system in a lossy two-mode cavity is studied, with the first mode being resonant to the electronic transition and the second one being nearly resonant due to Raman transitions. We derive analytical solutions for the dynamics of this system. For a properly chosen detuning of the second mode from the exact Raman resonance, we obtain conditions that are closely related to the phenomenon of Rabi resonance as it is well known in laser physics. Such resonances can be observed in the spontaneous emission spectra, where the spectrum of the second mode in the case of weak Ram…
The well-known laser-induced Rabi oscillations of a two-level atom are shown to be suppressed under certain conditions when the atom is entering a laser-illuminated region. For temporal Rabi oscillations the effect has two regimes: classical-like, at intermediate atomic velocities, and quantum at low velocities, associated respectively with the formation of incoherent or coherent internal states of the atom in the laser region. In the low velocity regime the laser projects the atom onto a pure internal state that can be controlled by detuning. Spatial Rabi oscillations are only suppressed in t…
In this paper, an analytical solution of the two-qubit Rabi model for the general case is presented. Furthermore, a comparison between the information entropies and the Von Neumann entropy $(ρ_{A})$ is given for some special values of the qubit-photon coupling constants in case of the detuning parameters. It is demonstrated that oscillations of the occupation probabilities $ρ_{11}, ρ_{22}, ρ_{33}$ and $ρ_{44}$ are equivalent to the case of the spontaneous emission. The occupation probability $ρ_{11}$ reaches the case of sudden death, when the detuning parameters $Δ_{2}$ equals zero.
First order Doppler effects are usually ignored in laser driven trapped ions when the recoil frequency is much smaller than the trapping frequency (Lamb-Dicke regime). This means that the central, carrier excitation band is supposed to be unaffected by vibronic transitions in which the vibrational number changes. While this is strictly true in the Lamb-Dicke limit (infinitely tight confinement), the vibronic transitions do play a role in the Lamb-Dicke regime. In this paper we quantify the asymptotic behaviour of their effect with respect to the Lamb-Dicke parameter. In particular, we give ana…
We report on the excitation of single molecules via narrow zero-phonon transitions using short laser pulses. By monitoring the Stokes-shifted fluorescence, we studied the excited state population as a function of the delay time, laser intensity, and frequency detuning. A pi-pulse excitation was demonstrated with merely 500 photons, and 5 Rabi cycles were achieved at higher excitation powers. Our findings are in good agreement with theoretical calculations and provide a first step toward coherent manipulation of the electronic states of single molecules with few photons.
Resilience to noise and to decoherence processes is an important ingredient for the implementation of quantum information processing, and quantum technologies. To this end, techniques such as pulsed and continuous dynamical decoupling have been proposed to reduce noise effects. In this paper, we suggest a new approach to implementing continuous dynamical decoupling techniques, that uses an extra control parameter; namely, the ability to shape the time dependence of the detuning. This approach reduces the complexity of the experimental setup, such that we are only left with noise originating fr…
The coherent dynamics of relaxing spin qubits driven by a classical bichromatic field comprising a strong resonant component and a weaker component with a frequency close to the strong-field Rabi frequency is studied. The double dressing by the bichromatic field modifies dephasing and dissipation processes. We demonstrate that detuning of the weaker-field frequency from the strong-field Rabi frequency prolongs the decay of Rabi oscillations between some doubly dressed states. The sensitivity of Rabi oscillations to the modified detuning-dependent relaxation is illustrated for nitrogen-vacancy …
We theoretically study the superradiant phase transition (SPT) in an indirect Rabi model, where both a two-level system and a single mode bosonic field couple to an auxiliary bosonic field. We find that the indirect spin-field coupling induced by the virtual excitation of the auxiliary field can allow the occurrence of a SPT at a critical point, and the influence of the so-called $A^2$ term in the normal Rabi model is naturally avoided. In the large detuning regime, we present the analytical expression of quantum critical point in terms of the original system parameters. The critical atom-fiel…
A quantum two level system coupled to a harmonic oscillator represents a ubiquitous physical system. New experiments in circuit QED and nano-electromechanical systems (NEMS) achieve unprecedented coupling strength at large detuning between qubit and oscillator, thus requiring a theoretical treatment beyond the Jaynes Cummings model. Here we present a new method for describing the qubit dynamics in this regime, based on an oscillator correlation function expansion of a non-Markovian master equation in the polaron frame. Our technique yields a new numerical method as well as a succinct approxima…
Here we use perturbation techniques based on the averaging method to investigate Rabi oscillations in cw and pulse-driven two-level systems (TLS's). By going beyond the rotating-wave approximation, especifically to second-order in perturbation, we obtain the Bloch-Siegert shift of the TLS resonant frequency, in which the resonant frequency increases with the driving field amplitude. This frequency shift implies that short resonant $π$-pulses in which the Rabi frequency is approximately 40\% or higher of the transition frequency do not achieve complete inversion in TLS's. Hence, guided by analy…
We consider the flavor transformation of neutrinos through oscillatory matter profiles. We show that the neutrino oscillation Hamiltonian in this case describes a Rabi system with an infinite number of Rabi modes. We further show that, in a given physics problem, the majority of the Rabi modes have too small amplitudes to be relevant. We also go beyond the rotating wave approximation and derive the relative detuning of the Rabi resonance when multiple Rabi modes with small amplitudes are present. We provide an explicit criterion of whether an off-resonance Rabi mode can affect the parametric f…
For a superconducting qubit driven to perform Rabi oscillations and coupled to a slow electromagnetic or nano-mechanical oscillator we describe previously unexplored quantum optics effects. When the Rabi frequency is tuned to resonance with the oscillator the latter can be driven far from equilibrium. Blue detuned driving leads to a population inversion in the qubit and a bi-stability with lasing behavior of the oscillator; for red detuning the qubit cools the oscillator. This behavior persists at the symmetry point where the qubit-oscillator coupling is quadratic and decoherence effects are m…
A unified diagrammatic approach to quantum transport in few-level junctions for bosonic and fermionic reservoirs: Application to the quantum Rabi model
The generalized Rabi model (gRM) with both one- and two-photon coupling terms has been successfully implemented in circuit quantum electrodynamics systems. In this paper, we examine theoretically multiphoton resonances in the gRM and derive their effective Hamiltonians. With different detunings in the system, we show that all three- to six-photon resonances can be achieved by involving two intermediate states. Furthermore, we study the interplay between multiphoton resonance and chiral transport of photon Fock states in a resonator junction with broken time-reversal symmetry. Depending on the …
Here we analyse cavity-mediated laser cooling for an experimental setup with an external trap which strongly confines the motion of a particle in the direction of the cavity axis. It is shown that the stationary state phonon number exhibits three sharp minima as a function of the atom-cavity detuning due to a direct atom-phonon-photon coupling term in the system Hamiltonian. These resonances have the same origin as the Mollow triplet in the resonance fluorescence of a laser-driven atomic system. It is shown that a laser-Rabi frequency-dependent atom-cavity detuning yields the lowest stationary…
We study the behavior of the Rabi oscillations of a driven central spin (qubit) coupled to an antiferromagnetic spin bath (environment). It is found that the decoherence behavior of the central spin depends on the detuning, driving strength, the qubit-bath coupling and an important factor, associated with the number of the coupled atoms, the detailed lattice structure, and the temperature of the environment. If the detuning exists, the Rabi oscillations may show the behavior of collapses and revivals; however, if the detuning is zero, such a behavior will not appear. We investigate the weighte…
The observable line shape of the spontaneous emission depends on the procedure of atom's excitation. The spectrum of radiation emitted by a two-level atom excited from the ground state by a pi pulse of the resonant pump field is calculated for the case when the Rabi frequency is much larger than the relaxation rate. It is shown that the central part of the spectral distribution has a standard Lorentzian form, whereas for detunings from the resonance that are larger than the Rabi frequency the spectral density falls off faster. The shape of the wings of the spectral line is sensitive to the for…
Collective Chirped STIRAP in a Pair of Three-Level Atoms: Dressed-Manifold Dynamics and Compensation of the Rydberg-Rydberg Interaction-Induced Detuning
When an atom strongly couples to a cavity, it can undergo coherent vacuum Rabi oscillations. Controlling these oscillatory dynamics quickly relative to the vacuum Rabi frequency enables remarkable capabilities such as Fock state generation and deterministic synthesis of quantum states of light, as demonstrated using microwave frequency devices. At optical frequencies, however, dynamical control of single-atom vacuum Rabi oscillations remains challenging. Here, we demonstrate coherent transfer of optical frequency excitation between a single quantum dot and a cavity by controlling vacuum Rabi o…
We study the Rabi model composed of three qubits coupled to a harmonic oscillator without involving the rotating-wave approximation. We show that the ground state of the three-qubit Rabi model can be analytically treated by using the transformation method, and the transformed ground state agrees well with the exactly numerical simulation under a wide range of qubit-oscillator coupling strengths for different detunings. We use the pairwise entanglement to characterize the ground-state entanglement between any two qubits and show that it has an approximately quadratic dependence on the qubit-osc…
Robust controlled-Z gate for Rydberg atoms based on level-crossing-free echoing rapid adiabatic passage
College of Physics and Electronic Engineering, Shanxi University（山西大学物理电子工程学院）；Collaborative Innovation Center of Extreme Optics, Shanxi University（山西大学极端光学协同创新中心）
QED-model for multichain coupled qubit system, proposed in \cite{Part1}, was confirmed by Raman scattering studies of quasi-1D carbon zigzag-shaped nanotubes (CZSNTs), produced by high energy ion beam modification of natural diamond single crystals. Multichain coupled qubit system represents itself Su-Schriffer-Heeger $σ$-polaron lattice, formed in CZSNTs plus quantized external electromagnetic (EM) field. New quantum optics phenomenon - Rabi waves, predicted in \cite{Slepyan_Yerchak} has experimentally been identified for the first time. It is shown, that Raman spectra in quasi-1D CZSNTs are …
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 performed quantum manipulations of the multi-level spin system S=5/2 of a Mn$^{2+}$ ion, by means of a two-tone pulse drive. The detuning between the excitation and readout radio frequency pulses allows one to select the number of photons involved in a Rabi oscillation as well as increase the frequency of this nutation. Thus detuning can lead to a resonant multi-photon process. Our analytical model for a two-photon process as well as a numerical generalization fit well the experimental findings, with implications in the use of multi-level spin systems as tunable solid state qubits.
We demonstrate coherent control of the optical transition of single Nitrogen-Vacancy defect centers in diamond. On applying short resonant laser pulses, we observe optical Rabi oscillations with a half-period as short as 1 nanosecond, an order of magnitude shorter than the spontaneous emission time. By studying the decay of Rabi oscillations, we find that the decoherence is dominated by laser-induced spectral jumps. By using a low-power probe pulse as a detuning sensor and applying post-selection, we demonstrate that spectral diffusion can be overcome in this system to generate coherent photon…
The extended quantum Rabi models make a significant contribution to understand the quantum nature of the atom-light interaction. We transform two kinds of extended quantum Rabi model, anisotropic Rabi model and asymmetric Rabi model, into rotating frame, and regard them as periodically driven quantum systems. The analytical solutions of the quasi-energy spectrum as well as the Floquet modes for both models are constructed by applying the Floquet theory and the high-frequency expansion, which is applied to the non-stroboscopic dynamics of physical observables such as atomic inversion, transvers…
A new heuristic model of interaction of an atomic system with a gravitational wave is proposed. In it, the gravitational wave alters the local electromagnetic field of the atomic nucleus, as perceived by the electron, which changes the energy of the system. The spectral decomposition of the wave function is calculated, from which the energy of the system can be obtained. The results suggest a shift in the energy difference of the atomic energy levels, which will induce a small detuning to any given resonant transition. The detuning increases with the quantum numbers of the levels, making the e…
For a transition $F_e=0\leftrightarrow F_g=1$ driven by a linearly polarized light and probed by a circularly light, quantum coherence effects are investigated. Due to the coherence between the drive Rabi frequency and Zeeman splitting, electromagnetically induced transparency, electromagnetically induced absorption, and the transition from positive to negative dispersion are obtained, as well as the populations coherently oscillating in a wide spectral region. At the zero pump-probe detuning, the subluminal and superluminal light propagation is predicted. Finally, coherent population trapping…
We demonstrate enhancement of the dispersive frequency shift in a coplanar waveguide resonator induced by a capacitively-coupled superconducting flux qubit in the straddling regime. The magnitude of the observed shift, 80 MHz for the qubit-resonator detuning of 5 GHz, is quantitatively explained by the generalized Jaynes-Cummings model which takes into account the contribution of the qubit higher energy levels. By applying the enhanced dispersive shift to the qubit readout, we achieved 90% contrast of the Rabi oscillations which is mainly limited by the energy relaxation of the qubit.
In circuit QED, protocols for quantum gates and readout of superconducting qubits often rely on the dispersive regime, reached when the qubit-photon detuning Δ is large compared to their mutual coupling strength. For qubits including the Cooper-pair box and transmon, selection rules dramatically restrict the contributions to dispersive level shifts χ. By contrast, without selection rules many virtual transitions contribute to χ and can produce sizable dispersive shifts even at large detuning. We present theory for a generic multi-level qudit capacitively coupled to one or multiple harmonic mod…
We investigate how the quantum control of a two-level system (TLS) coupled to photons can modify and tune the TLS's photon absorption spectrum. Tuning and controlling the emission and the absorption is of much interest e.g.\ for the development of efficient interfaces between stationary and flying qubits in modern architectures for quantum computation and quantum communication. We consider the periodic pulse control, where the TLS is subjected to a periodic sequence of the near-resonant Rabi driving pulses, each pulse implementing a 180$^\circ$ rotation. For small inter-pulse delays, the absor…
We investigate the dynamics of a strongly-driven, microwave-dressed, donor-bound electron spin qubit in silicon. A resonant oscillating magnetic field $B_1$ is used to dress the electron spin and create a new quantum system with a level splitting proportional to $B_1$. The dressed two-level system can then be driven by modulating the detuning $Δν$ between the microwave source frequency $ν_{\rm MW}$ and the electron spin transition frequency $ν_e$ at the frequency of the level splitting. The resulting dressed qubit Rabi frequency $Ω_{Rρ}$ is defined by the modulation amplitude, which can be mad…
We report two novel effects in an inhomogeneous ensemble of two-level systems driven by an external field. First, we observe a rigidity of the oscillation frequency: the dominant Rabi oscillation frequency does not change with the frequency of the driving field, in contrast to the well-known law of Rabi frequency increase with growing detuning of the driving field. Second, we observe a time-dependent frequency shift of the ensemble-averaged oscillation. We show that these effects follow from the inhomogeneity of the two-level splitting across the ensemble, allowing for a distribution of local …
We investigate the quantum noise properties of a weakly nonlinear Duffing resonator in the deep quantum regime, where only few quanta are excited. This regime is dominated by the appearance of coherent multiphoton resonances in the nonlinear response of the resonator to the modulation. We determine simple expressions for the photon noise spectrum and find that the multiphoton resonances also induces a multiple peak structure in that noise. When the corresponding multiphoton Rabi oscillations are underdamped, zero temperature quantum fluctuations determine comparable populations of all quasiene…
In this work we present a scheme to control the optical dipole trap potential in an N-type four-level atomic system by using chirped femtosecond Gaussian pulses. The spatial size of the trap can be well controlled by tuning the beam waist of the Gaussian pulse and the detuning frequency. The trapping potential splits with increasing Rabi frequency about the center of the trap, a behavior analogous to the one observed experimentally in the context of trapping of nanoparticles with femtosecond pulses. An attempt is made to explain the physics behind this phenomenon by studying the spatial probab…
