Precise quantum control relies on a deep understanding of the dynamics of quantum systems under external drives. This study investigates the impact of anharmonicity on qubit dynamics under conditions typical for two-qubit entangling gates activated by weak near-resonant microwave drives. We measure the Rabi oscillation frequency as a function of drive amplitude and detuning. Our results reveal a linear dependence of the squared Rabi frequency on the squared drive amplitude, which relates to the ratio of detuning to anharmonicity, demonstrating strong agreement between experimental data and analytical predictions. Additionally, we analyze the leakage and phase errors arising from inaccurate Rabi frequency adjustments in the CZ gate implementation on fluxonium qubits driven by a microwave signal applied to the coupler.
With a resonant amplitude-modulation field on two Rydberg atoms, we propose a Rydberg antiblockade (RAB) regime, where the Rabi oscillation between collective ground and excited states is induced. A controlled-Z gate can be yielded through a Rabi cycle. Further, several common issues of the RAB gates are solved by modifying the parameter relation. The gate fidelity and the gate robustness against the control error are enhanced with a shaped pulse. The requirement of control precision of the Rydberg-Rydberg interaction strength is relaxed. In addition, the atomic excitation is restrained and th…
In circuit QED, a Rabi model can be derived by truncating the Hilbert space of the anharmonic qubit coupled to a linear, reactive environment. This truncation breaks the gauge invariance present in the full Hamiltonian. We analyze the determination of an optimal gauge such that the differences between the truncated and the full Hamiltonian are minimized. Here, we derive a simple criterion for the optimal gauge. We find that it is determined by the ratio of the anharmonicity of the qubit to an averaged environmental frequency. We demonstrate that the usual choices of flux and charge gauge are n…
We consider a generalized Rabi model formed by two identical qubits interacting with a common oscillator mode. In the near resonance configuration where the oscillator frequency is close to the transition frequency of the qubit, we determine the ground state of the model approximately by using a variational method and a transformation method. Both methods are shown to provide good agreement with the exact numerical ground state for a range of coupling strength in the ultrastrong regime. In addition, we indicate how the accuracy of the approximation can be further improved by using perturbation…
In this report, we have studied exceptional spectra of the two-qubit quantum Rabi model in two situations. Firstly, an exceptional spectra is achieved in resonant condition, in which the frequencies of two qubit and photon field satisfy resonant relation. With transformed rotating-wave approximation (TRWA) method, the Rabi model can be mapped into the solvable formation in qubit-photon Fock states space. Based on the quantum supperconducting circuits experiment setup, the best value range of the system parameters are discussed. In the resonant station working window, the energy spectrums are c…
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…
The quantum Rabi oscillations in a coherently driven quantum dot embedded in a high-Q doubly resonant semiconductor micro-cavity in the presence of a strong second-order nonlinear medium is investigated theoretically. It is shown that the second order nonlinearity effect the Rabi oscillations in a significant manner.
The Rabi Hamiltonian, describing the interaction between a two-level atomic system and a single cavity mode of the electromagnetic field, is one of the fundamental models in quantum optics. The model becomes exactly solvable by considering an atom without permanent dipole moments, whose excitation energy is quasi-resonant with the cavity photon energy, and by neglecting the non resonant (counter-rotating) terms. In this case, after including the decay of either the atom or the cavity mode to a continuum, one is able to derive the well-known phenomenology of quasi-resonant transitions, includin…
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 have numerically obtained theoretical results for the collapse and the revival of the quantum Rabi oscillations for low average number of coherent photons injected on a two-level system in a lossy resonant cavity. We have adopted the multimode Jaynes-Cummings model for the same and especially treated the ``Ohmic" loss to the walls of the cavity, the leakage from the cavity, and the loss due to the spontaneous emission through the open surface of the cavity. We have compared our results with the experimental data obtained by Brune et al [Phys. Rev. Lett. 76, 1800 (1996)] in this regard.
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…
Optically controlled coherent dynamics of charge (excitonic) degrees of freedom in a semiconductor quantum dot under the influence of lattice dynamics (phonons) is discussed theoretically. We show that the dynamics of the lattice response in the strongly non-linear regime is governed by a semiclassical resonance between the phonon modes and the optically driven dynamics. We stress on the importance of the stability of intermediate states for the truly coherent control.
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 considered one-dimensional quantum chains of two-level Fermi particles coupled via the tunneling driven both by ac and dc fields in the regimes of strong and ultrastrong coupling. The frequency of ac field is matched with the frequency of the quantum transition. Based on the fundamental principles of electrodynamics and quantum theory, we developed a general model of quantum dynamics for such interactions. We showed that the joint action of ac and dc fields leads to the strong mutual influence of Rabi- and Bloch oscillations one to another. We focused on the regime of ultrastrong coupling, …
We investigate the applicability of the two major approximations which are most commonly employed in the study of the quantum Rabi model, namely the description of a resonant cavity mode as a single-mode quantized field and the use of the rotating wave approximation. Starting from the Hamiltonian of a two-level system interacting with a multi-mode quantized field, we perform the canonical transformation of the field operators. This allows one to partition the Hamiltonian of the system into two parts. The first part is the interaction of the two-level system with a single collective field mode,…
We study the dynamic sensitivity of the quantum Rabi model, which exhibits quantum criticality in the finite-component-system case. This dynamic sensitivity can be detected by introducing an auxiliary two-level atom far-off-resonantly coupled to the cavity field of the quantum Rabi model. We find that when the quantum Rabi model goes through the critical point, the auxiliary atom experiences a sudden decoherence, which can be characterised by a sharp decay of the Loschmidt echo. Our scheme will provide a reliable way to observe quantum phase transition in ultrastrongly coupled quantum systems.
We simulate Shor's algorithm on an Ising spin quantum computer. The influence of non-resonant effects is analyzed in detail. It is shown that our ``$2πk$''-method successfully suppresses non-resonant effects even for relatively large values of the Rabi frequency.
We study the nonlinear dynamics of trapped-ion models far away from the Lamb-Dicke regime. This nonlinearity induces a sideband cooling blockade, stopping the propagation of quantum information along the Hilbert space of the Jaynes-Cummings and quantum Rabi models. We compare the linear and nonlinear cases of these models in the ultrastrong and deep strong coupling regimes. Moreover, we propose a scheme that simulates the nonlinear quantum Rabi model in all coupling regimes. This can be done via off-resonant nonlinear red and blue sideband interactions, yielding applications as a dynamical qua…
An exact analytic solution is presented for coherent resonant excitation of a two-state quantum system driven by a time-dependent pulsed external field with a hyperbolic-secant shape in the presence of dephasing. Analytic results are derived for the amplitude and the phase shift of the damped Rabi oscillations.
In a direct two-level qubit system, when the Rabi frequency is comparable to the resonance frequency, the rotating wave approximation is not appropriate. In this case, the Rabi oscillation is accompanied by another oscillation at twice the frequency of the driving field, the so called Bloch-Siegert oscillation (BSO), which depends on the initial phase of the driving field. This oscillation may restrict the precise rotation of a qubit made of direct two-level system. Here, we show that in case of an effectively two-level lambda system, the BSO is inherently negligible, implying a greater precis…
We examine cold atomic collisions within a resonant optical cavity. The quantized cavity mode can be used to manipulate the collisions between the cold atoms, such that periodic exchange of excitations between the atoms and the electromagnetic field strongly alters the collision dynamics. A colliding pair of atoms can thereby oscillate between its ground and excited states during the collision time. Using a semiclassical model, it can be predicted that such Rabi-like oscillations are revealed in the atomic trap-loss probabilities, which show maxima and minima as a function of the detuning betw…
We study quantum thermalization and thermal entanglement in the open quantum Rabi model (QRM), in which a two-level system and a single-mode bosonic field are coupled to either two individual heat baths or a common heat bath. By treating the QRM as an effective multilevel system and deriving global quantum master equations in the eigenstate representation of the QRM, we study the physical conditions for quantum thermalization of the open QRM. It is found that, in the individual heat-bath case, the QRM can only be thermalized when either the two heat baths have the same temperature or the QRM i…
In this work we report the modification of the normal Auger line shape under the action of an intense x-ray radiation. Under strong Rabi-type coupling of the core, the Auger line profile develops into a doublet structure with an energy separation mainly determined by the relative strength of the Rabi coupling. In addition, we find that the charge resolved ion yields can be controlled by judicious choice of the x-ray frequency.
We study quantum optics with the atoms coupled to the quantized electromagnetic (EM) field in a non-inertial reference frame by making use of quantum field theory in curved spacetime. We rigorously establish the microscopic model for a two-level atom interacting with the quantized EM field in a rotating ring cavity by deriving a Jaynes-Cummings (JC) type Hamiltonian. Due to the two fold degeneracy of the ring cavity modes, the Rabi splitting exhibits three rather than two resonant frequency peaks. We find that the heights of the two side peaks show a sensitive linear dependence on the rotating…
We have investigated the microwave response of a transmon qubit coupled directly to a transmission line. In a transmon qubit, owing to its weak anharmonicity, a single driving field may generate dressed states involving more than two bare states. We confirmed the formation of three-state dressed states by observing all of the six associated Rabi sidebands, which appear as either amplification or attenuation of the probe field. The experimental results are reproduced with good precision by a theoretical model incorporating the radiative coupling between the qubit and the microwave.
In the present paper we show that the Hamiltonian describing the resonant interaction of $N$ two-level systems with a single-mode electromagnetic quantum field in the Coulomb gauge can be diagonalized with a high degree of accuracy using a simple basis set of states. This allows one to find an analytical approximation for the eigenvectors and eigenvalues of the system, which interpolates the numerical solution in a broad range of the coupling constant values. In addition, the introduced basis states provide a regular way of calculating the corrections and estimating the convergence to the exac…
We present a theoretical study of a quantum regime of the resistive (whirling) state of dc driven anisotropic single plaquette containing three small Josephson junctions. The current-voltage characteristics of such a system display resonant steps that are due to the resonant interaction between the time dependent Josephson current and the excited electromagnetic oscillations (EOs). The voltage positions of the resonances are determined by the quantum interband transitions of EOs. We show that in the quantum regime as the system is driven on the resonance, coherent Rabi oscillations between the…
The simple resonant Rabi oscillation of a two-level system in a single-mode coherent field reveals complex features at the mesoscopic scale, with oscillation collapses and revivals. Using slow circular Rydberg atoms interacting with a superconducting microwave cavity, we explore this phenomenon in an unprecedented range of interaction times and photon numbers. We demonstrate the efficient production of `cat' states, quantum superposition of coherent components with nearly opposite phases and sizes in the range of few tens of photons. We measure cuts of their Wigner functions revealing their qu…
We discuss a cavity-QED scheme to deterministically generate entangled photons pairs by using a three-level atom successively coupled to two single longitudinal mode high-Q cavities presenting polarization degeneracy. The first cavity is prepared in a well defined Fock state with two photons with opposite circular polarizations while the second cavity remains in the vacuum state. A half-of-a-resonant Rabi oscillation in each cavity transfers one photon from the first to the second cavity, leaving the photons entangled in their polarization degree of freedom. The feasibility of this implementat…
Optically-driven Rabi oscillations of single electron spins in a diamond nitrogen vacancy center are realized with two Raman-resonant optical pulses that are detuned from the respective dipole optical transitions. The Rabi oscillations are nuclear-spin selective and are robust against rapid decoherence of the underlying optical transitions, opening the door to generating phonon-mediated spin entanglement in an optically-driven spin-phonon system. A direct comparison between the Rabi oscillations and simulated Raman adiabatic passage along with a detailed theoretical analysis provide a wealth o…
Under resonant conditions, a long sequence of landau-zener transitions can lead to Rabi oscillations. Using a nitrogen-vacancy (NV) center spin in diamond, we investigated the interference between more than 100 Landau-Zener processes. We observed the new type of Rabi oscillations of the electron spin resulting from the interference between successive Landau-Zener processes in various regimes, including both slow and fast passages. The combination of the control techniques and the favorable coherent properties of NV centers provides an excellent experimental platform to study a variety of quant…
State selective preparation and manipulation of discrete-level quantum systems such as atoms, molecules or quantum dots is a the ultimate tool for many diverse fields such as laser control of chemical reactions, atom optics, high-precision metrology and quantum computing. Rabi oscillations are one of the simplest, yet potentially quite useful mechanisms for achieving such manipulation. Rabi theory establishes that in the two-level systems resonant drive leads to the periodic and complete population oscillations between the two system levels. In this paper an analytic optimization algorithm for…
We considered one-dimensional chain of the two-level quantum systems coupled via tunneling. The chain is driven by the superposition of dc and ac fields in the strong coupling regime. Based on the fundamental principles of electrodynamics and quantum theory, we developed a generalized model of quantum dynamics for such interactions, free of rotating wave approximation (RWA). The system of motion equations was studied numerically. We analyzed the dynamics and spectra of inversion density, dipole current density and tunneling current density. In the case of resonant interaction with ac-component…
Under resonant irradiation, a quantum system can undergo coherent (Rabi) oscillations in time. We report evidence for such oscillations in a _continuously_ observed three-Josephson-junction flux qubit, coupled to a high-quality tank circuit tuned to the Rabi frequency. In addition to simplicity, this method of_Rabi spectroscopy_ enabled a long coherence time of about 2.5 microseconds, corresponding to an effective qubit quality factor \~7000.
We consider the dynamics of atomic and field coherent states in the non-resonant Dicke model. At weak coupling an initial product state evolves into a superposition of multiple field coherent states that are correlated with the atomic configuration. This process is accompanied by the buildup and decay of atom-field entanglement and leads to the periodic collapse and revival of Rabi oscillations. We provide a perturbative derivation of the underlying dynamical mechanism that complements the rotating wave approximation at resonance. The identification of two different time scales explains how th…
We present theoretical transmission spectra of a strongly driven, damped, flux qubit coupled to a dissipative resonator in the ultrastrong coupling regime. Such a qubit-oscillator system, described within a dissipative Rabi model, constitutes the building block of superconducting circuit QED platforms. The addition of a strong drive allows one to characterize the system properties and study novel phenomena, leading to a better understanding and control of the qubit-oscillator system. In this work, the calculated transmission of a weak probe field quantifies the response of the qubit, in freque…
Rabi oscillations are periodic modulations of populations in two-level systems interacting with a time-varying field. They are ubiquitous in physics with applications in different areas such as photonics, nano-electronics, electron microscopy, and quantum information. While the theory developed by Rabi was intended for fermions in gyrating magnetic fields, Autler and Townes realized that it could also be used to describe coherent light-matter interaction within the rotating wave approximation\cite. Although intense nanometer-wavelength light-sources have been available for more than a decade, …
We have generalized Einstein coefficients and rate equations from quantum field theoretic point of view by bringing the fundamental processes and the quantum Rabi oscillation in a single footing for the light-matter interactions for nonzero Rabi frequency. We have analytically obtained multimode Jaynes-Cummings model results for the quantum Rabi oscillations of a two-level system in a lossy resonant cavity containing (i) thermal photons and (ii) injected photons of a coherent field. We have renormalized the coupling constant for the light-matter interactions for these cases. Our results match …
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 consider joint effects of tunneling and spin-orbit coupling on driven by electric field spin dynamics in a double quantum dot with a multi-level resonance scenario. We demonstrate that tunneling plays the crucial role in the formation of the Rabi-like spin-flip transitions. In contrast to the linear behavior for weak electric fields, the spin flip rate becomes much smaller than expected for the two-level model and shows oscillating dependence on the driving field amplitude in stronger fields. In addition, the full spin flip is very difficult to achieve in a multi-level resonant system. Thes…
We report coherent interactions within an ensemble of silicon-vacancy color centers in diamond. The interactions are ascribed to resonant dipole-dipole coupling. Further, we demonstrate control over resonant center pairs by using a driving optical pulse to induce collective, interaction-enabled Rabi-oscillations in the ensemble. Non-resonant center pairs do not undergo collective oscillations.
Topological phases of matter became a new standard to classify quantum systems in many cases, yet key quantities like the quantum geometric tensor providing local information about topological properties are still experimentally hard to access. In non-Abelian systems this accessibility to geometric properties can be even more restrictive due to the degeneracy of the states. We propose universal protocols to determine quantum geometric properties in non-Abelian systems. First, we show that for a weak resonant driving of the local parameters the coherent Rabi oscillations are related to the quan…
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 f…
Strong molecule-light interaction enables the control of molecular structures and dynamical processes. A model with strong laser drive is proposed to greatly enhance the intermolecular distance of resonant energy transfer, where the molecules are strongly driven by an optical cavity. The optimal Rabi frequency and quantum yield of energy transfer are observed, resulting from the trade off between dipole-dipole interaction and molecule-cavity coupling. When the strong drive at certain Rabi frequency is applied, a larger spatial range of effective energy transfer and a slower decay rate with the…
From the high vibrational dipolar strength offered by molecular liquids, we demonstrate that a molecular vibration can be ultra-strongly coupled to multiple IR cavity modes, with Rabi splittings reaching $24\%$ of the vibration frequencies. As a proof of the ultra-strong coupling regime, our experimental data unambiguously reveal the contributions to the polaritonic dynamics coming from the anti-resonant terms in the interaction energy and from the dipolar self-energy of the molecular vibrations themselves. In particular, we measure the opening of a genuine vibrational polaritonic bandgap of c…
Nonlinear dynamics of establishment of electron-hole coherent superpositions states in graphene by multiphoton resonant excitation of interband transitions in laser fields is considered. The single-particle time dependent density matrix for such a quantized system is calculated in the multiphoton resonant approximation. The dependence of Rabi oscillations of Fermi-Dirac sea in graphene on the time, momentum, and photon number at multiphoton laser-excitation is analyzed.
We report results of spectroscopic measurements and time-domain measurements of a superconducting flux qubit. The dc superconducting quantum interference device (SQUID), used for readout of the qubit, and a shunt capacitor formed an LC resonator generating a SQUID plasma mode. Higher-order red and blue sidebands were observed in a simple measurement scheme because the resonant energy of the resonator, 600 MHz, was comparable to the thermal energy. We also observed Rabi oscillations on the carrier transition and the first-order sideband transitions. Because the qubit was coupled to a single arm…
