In the present work the Rabi Problem, involving the response of a spin 1/2 particle subjected to a magnetic field, is considered in a second quantized approach. In this concrete physical scenario, we show that the second quantization procedure can be applied directly in a non-covariant theory. The proposed development explicits not only the relation between the full quantum treatment of the problem and the semiclassical Rabi model, but also the connection of these approaches with the Jaynes-Cummings model. The consistency of the method is checked in the semiclassical limit. The treatment is then extended to the matter component of the Rabi problem so that the Schrödinger equation is directly quantized. Considering the spinorial field, the appearance of a negative energy sector implies a specific identification between Schrödinger's and Maxwell's theories. The generalized theory is consistent, strictly quantum and non-relativistic.
We model recent experiments on living sulphur bacteria interacting with quantised light, using the Dicke model. The strong coupling achieved between the bacteria and the light indicates that during the experiment the bacteria (treated as dipoles) and the quantized light are entangled. The vacuum Rabi splitting, which was measured in the experiment for a range of different parameters, can be used as an entanglement witness.
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 consider…
The dissipative response of a quantum system upon a time-dependent drive can be exploited as a probe of its geometric and topological properties. In this work, we explore the implications of such phenomena in the context of two-dimensional gases subjected to a uniform magnetic field. It is shown that a filled Landau level exhibits a quantized circular dichroism, which can be traced back to its underlying non-trivial topology. Based on selection rules, we find that this quantized circular dichroism can be suitably described in terms of Rabi oscillations, whose frequencies satisfy simple quantiz…
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 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,…
QED-model for the multichain qubit system with interactions of qubits and chains between themselves on the example of the system of $σ$-polarons in carbon zigzag nanotubes, interacting with quantized EM-field, is considered analytically. The possibility of experimental detection of Rabi waves in conventional stationary optical experiments for any quasi-1D system with strong electron-photon interaction is predicted.
We present a stability analysis of an interacting two-species Bose-Einstein condensate driven by a quantized field in the semi-classical limit. Transitions from Rabi to Josephson dynamics are identified depending on both the inter-atomic interaction to field-condensate coupling ratio and the ratio between the total excitation number and the condensate size. The quantized field is found to produce asymmetric dynamics for symmetric initial conditions for both Rabi and Josephson oscillations.
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 develop a scheme to construct the Hamiltonians of the lambda, vee and cascade type of three-level configurations using the generators of SU(3) group. It turns out that this approach provides a well defined selection rule to give different Hamitonians for each configurations. The lambda and vee type configurations are exactly solved with different initial conditions while taking the two-mode classical and quantized fields . For the classical field, it is shown that the Rabi oscillation of the lambda model is similar to that of the vee model and the dynamics of the vee model can be recovered …
The interaction of a two-level atom with a single-mode quantized field is one of the simplest models in quantum optics. Under the rotating wave approximation, it is known as the Jaynes-Cummings model and without it as the Rabi model. Real-world realizations of the Jaynes-Cummings model include cavity, ion trap and circuit quantum electrodynamics. The Rabi model can be realized in circuit quantum electrodynamics. As soon as nonlinear couplings are introduced, feasible experimental realizations in quantum systems are drastically reduced. We propose a set of two photonic lattices that classically…
We have exactly solved a model of equidistant cascade four-level system interacting with a single-mode radiation field both semiclassically and quantum mechanically by exploiting its similarity with Jaynes-Cummings model. For the classical field, it is shown that the Rabi oscillation of the system initially in the first level (second level) is similar to that of the system when it is initially in the fourth level (third level). We then proceed to solve the quantized version of the model where the dressed state is constructed by using a six parameter four-dimensional matrix and show that the sy…
The coupling of a two-level system with an electromagnetic field, whose fully quantized version is the quantum Rabi model, is among the central topics of quantum physics. When the coupling strength becomes large enough that the field mode frequency is reached, the deep strong coupling regime is approached, and excitations can be created from the vacuum. Here we demonstrate a periodic variant of the quantum Rabi model in which the two-level system is encoded in the Bloch band structure of cold rubidium atoms in optical potentials. With this method we achieve a Rabi coupling strength of 6.5 time…
We consider multiphoton dynamics of a quantum system composed of a three-state atom (a qutrit) and a single-mode photonic field in the ultrastrong and deep strong coupling regimes, when the coupling strength is comparable to or larger than the oscillator energy scale. We assume a qutrit to be in a polar-$Λ$ configuration in which two lower levels have mean dipole moments. Direct multiphoton resonant transitions revealing generalized Rabi oscillations, collapse, and revivals in atomic excitation probabilities for the ultrastrong couplings are studied. In the deep strong coupling regime particul…
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…
We present an analytical approach to the problem of the multiphoton absorption and Rabi oscillations in an armchair graphene nanoribbon (AGNR) in the presence of a time-oscillating strong electric field induced by a light wave directed parallel to the ribbon axis. The two-dimensional Dirac equation for the massless electron subject to the ribbon confinement is employed. In the resonant approximation the electron-hole pair production rate, associated with the electron transitions between the valence and conduction size-quantized subbands, the corresponding multiphoton absorption coefficient and…
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…
Techniques based on continued fractions to compute numerically the spectrum of the quantum Rabi model are reviewed. They are of two essentially different types. In the first case, the spectral condition is implemented using a representation in the infinite-dimensional Bargmann space of analytic functions. This approach is shown to approximate the correct spectrum of the full model if the continued fraction is truncated at sufficiently high order. In the second case, one considers the limit of a sequence of models defined in finite-dimensional state spaces. Contrary to the first, the second app…
We study the coupled translational, electronic, and field dynamics of the combined system "a two-level atom + a single-mode quantized field + a standing-wave ideal cavity". We derive Hamilton -- Schrödinger equations for probability amplitudes and averaged position and momentum of a point-like atom interacting with the quantized field in a standing-wave cavity. They constitute, in general, an infinite-dimensional set of equations with an infinite number of integrals of motion which may be reduced to a dynamical system with four degrees of freedom if the quantized field is supposed to be initia…
The Kolmogorov complexity of a physical state is the minimal physical resources required to reproduce that state. We define a second quantized quantum Turing machine and use it to define second quantized Kolmogorov complexity. There are two advantages to our approach - our measure of second quantized Kolmogorov complexity is closer to physical reality and unlike other quantum Kolmogorov complexities it is continuous. We give examples where second quantized and quantum Kolmogorov complexity differ.
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.
We systematically study the interaction between two quantized optical fields and a cyclic atomic ensemble driven by a classic optical field. This so-called atomic cyclic ensemble consists of three-level atoms with Delta-type transitions due to the symmetry breaking, which can also be implemented in the superconducting quantum circuit by Yu-xi Liu et al. [Phys. Rev. Lett. 95, 087001 (2005)]. We explore the dynamic mechanisms to creating the quantum entanglements among photon states, and between photons and atomic collective excitations by the coherent manipulation of the atom-photon system. It …
The stability analysis of a generalized Dicke model, in the semi-classical limit, describing the interaction of a two-species Bose-Einstein condensate driven by a quantized field in the presence of Kerr and spontaneous parametric processes is presented. The transitions from Rabi to Josephson dynamics are identified depending on the relative value of the involved parameters. Symmetry-breaking dynamics are shown for both types of coherent oscillations due to the quantized field and nonlinear optical processes.
The Berry phase (BP) in a quantized light field demonstrated more than a decade ago (Phys. Rev. Lett. 89, 220404) has attracted considerable attentions, since it plays an important role in the cavity quantum electrodynamics. However, it is argued in a recent paper ( Phys. Rev. Lett. 108, 033601) that such a BP is just due to the rotating wave approximation (RWA) and the relevant BP should vanish beyond this approximation. Based on a consistent analysis we conclude in this letter that the BP in a generic Rabi model actually exists, no matter whether the RWA is applied. The existence of BP is al…
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 …
The analytical solution of the task of the interaction of quantized EM-field with multichain quasionedimensional axially symmetric qubit system by taking into account both the intrachain and interchain qubit coupling has been obtained for the first time. The appearance of additional lines in optical spectra of quasionedimensional systems strongly interacting with EM-field is predicted. They are result of nonstationary registration conditions, to be consequence of Rabi wave packet formation and correspond to Fourier transformation of revival part of Rabi wave packets in temporal dependence of t…
Gauge invariance is the cornerstone of modern quantum field theory. Recently, it has been shown that the quantum Rabi model, describing the dipolar coupling between a two-level atom and a quantized electromagnetic field, violates this principle. This widely used model describes a plethora of quantum systems and physical processes under different interaction regimes. In the ultrastrong coupling regime, it provides predictions which drastically depend on the chosen gauge. This failure is attributed to the finite-level truncation of the matter system. We show that a careful application of the gau…
The quantum Rabi model (QRM) with linear coupling between light mode and qubit exhibits the analog of a second order phase transition for vanishing mode frequency which allows for criticality-enhanced quantum metrology in a few-body system. We show that the QRM including a non-linear coupling term exhibits much higher measurement precisions due to its first order like phase transition at \emph{finite} frequency, avoiding the detrimental slowing-down effect close to the critical point of the linear QRM. When a bias term is added to the Hamiltonian, the system can be used as a fluxmeter or magne…
Recently there have been some controversies about the criterion of the adiabatic approximation. It is shown that an approximate diagonalization of the effective Hamiltonian in the second quantized formulation gives rise to a reliable and unambiguous criterion of the adiabatic approximation. This is illustrated for the model of Marzlin and Sanders and a model related to the geometric phase which can be exactly diagonalized in the present sense.
We describe methods for simulating general second-quantized Hamiltonians using the compact encoding, in which qubit states encode only the occupied modes in physical occupation number basis states. These methods apply to second-quantized Hamiltonians composed of a constant number of interactions, i.e., linear combinations of ladder operator monomials of fixed form. Compact encoding leads to qubit requirements that are optimal up to logarithmic factors. We show how to use sparse Hamiltonian simulation methods for second-quantized Hamiltonians in compact encoding, give explicit implementations f…
Semiconductor microcavities in the strong-coupling regime exhibit an energy scale in the THz frequency range, which is fixed by the Rabi splitting between the upper and lower exciton-polariton states. While this range can be tuned by several orders of magnitude using different excitonic medium, the transition between both polaritonic states is dipole forbidden. In this work we show that in Cadmium Telluride microcavities, the Rabi-oscillation driven THz radiation is actually active without the need for any change in the microcavity design. This feature results from the unique resonance conditi…
We study two models describing the interaction of a two-level system with two quantum field modes. The first one is equivalent to a dissipative two-state system with just two boson fields in the absence of tunneling. The second describes two orthogonal fields interacting with the corresponding orthogonal dipoles of a two-level system. We show that both models present a partial two-mode $SU(2)$ symmetry and that they can be solved in the exceptional case of resonant fields. We study their ground state configurations, that is, we find the quantum precursors of the corresponding semi-classical ph…
The Kolmogorov complexity of a string is the length of its shortest description. We define a second quantised Kolmogorov complexity where the length of a description is defined to be the average length of its superposition. We discuss this complexity's basic properties. We define the corresponding prefix complexity and show that the inequalities obeyed by this prefix complexity are also obeyed by von Neumann entropy.
Second-quantized approach to the study of Halperin state in fractional quantum Hall effect
College of Physics and Electronic Science, Hubei Normal University（湖北师范大学物理与电子科学学院）；Hubei Key Laboratory of Photoelectric Materials and Devices, Hubei Normal University（湖北师范大学光电材料与器件湖北省重点实验室）
We investigate first- and second-order quantum phase transitions of the anisotropic quantum Rabi model, in which the rotating- and counter-rotating terms are allowed to have different coupling strength. The model interpolates between two known limits with distinct universal properties. Through a combination of analytic and numerical approaches we extract the phase diagram, scaling functions, and critical exponents, which allows us to establish that the universality class at finite? anisotropy is the same as the isotropic limit. We also reveal other interesting features, including a superradian…
We present a method for encoding second-quantized fermionic systems in qubits when the number of fermions is conserved, as in the electronic structure problem. When the number $F$ of fermions is much smaller than the number $M$ of modes, this symmetry reduces the number of information-theoretically required qubits from $Θ(M)$ to $O(F\log M)$. In this limit, our encoding requires $O(F^2\log^4 M)$ qubits, while encoded fermionic creation and annihilation operators have cost $O(F^2\log^5 M)$ in two-qubit gates. When incorporated into randomized simulation methods, this permits simulating time-evo…
We investigate a one-dimensional Rabi-Hubbard type of model, arranged such that a qdot is sandwiched between every cavity. The role of the qdot is to transmit photons between neighboring cavities, while simultaneously acting as a photon non-linearity. We consider three-level qdots in the $Λ$ configuration, where the left and right leg couples exclusively to the left or right cavity. This non-commuting interaction leads to two highly entangled incompressible phases, separated by a second order quantum phase transition: the qdot degrees-of-freedom act as a dynamical lattice for the photons and a…
We generalize the Unruh-DeWitt detector model to second quantization. We illustrate this model by applying it to an excited particle in a superposition of relativistic velocities. We calculate, to first order, how its decay depends on whether its superposition of velocities is coherent or incoherent. Further, we generalize the framework of quantum reference frames to allow transformations to the rest frames of second-quantized Unruh DeWitt detectors. As an application, we show how to transform into the rest frame of a decaying particle that, in the laboratory frame, is in a linear superpositio…
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…
We explore an extended quantum Rabi model describing the interaction between a two-mode bosonic field and a three-level atom. Quantum phase transitions of this few degree of freedom model is found when the ratio $η$ of the atom energy scale to the bosonic field frequency approaches infinity. An analytical solution is provided when the two lowest-energy levels are degenerate. According to it, we recognize that the phase diagram of the model consists of three regions: one normal phase and two superradiant phases. The quantum phase transitions between the normal phase and the two superradiant pha…
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 develop a framework that provides a straightforward approach to fully exploit the permutational symmetry of identical multi-level systems. By taking into account the permutational symmetry, we outline a simple scheme that allows to map the dynamics of $N$ identical $d$-level systems to the dynamics of $d$ bosonic modes with $N$ particles, achieving an exponential reduction on the dimensionality of the problem in a simple and straightforward way. In particular, we consider the Lindblad dynamics of several identical multi-level systems interacting with a common subsystem under the action of c…
Nonlocal quantum fluids emerge as dark-matter models and tools for quantum simulations and technologies. However, strongly nonlinear regimes, like those involving multi-dimensional self-localized solitary waves, are marginally explored for what concerns quantum features. We study the dynamics of 3D+1 solitons in the second-quantized nonlocal nonlinear Schroedinger-Newton equation. We theoretically investigate the quantum diffusion of the soliton center of mass and other parameters, varying the interaction length. 3D+1 simulations of the Ito partial differential equations arising from the posit…
Recent electron spin resonance experiments on CaWO$_4$:Gd$^{3+}$ and on other magnetic impurities have demonstrated that sustained Rabi oscillations can be created by driving a magnetic moment with a microwave field frequency slightly larger than the Larmor frequency and tuned to the Floquet resonance together with another microwave field (image drive). These observations are confirmed by the new experimental results reported in this paper. We investigate several mechanisms of decoherence and dissipation by using a combination of numerical and analytical techniques. The first microscopic model…
In recent years, the import of quantum information techniques in quantum gravity opened new perspectives in the study of the microscopic structure of spacetime. We contribute to such a program by establishing a precise correspondence between the quantum information formalism of tensor networks (TN), in the case of projected entangled-pair states (PEPS) generalised to a second-quantized framework, and group field theory (GFT) states, and by showing how, in this quantum gravity approach, discrete spatial manifolds arise as entanglement patterns among quanta of space, having a dual representation…
We describe an algebra G of diagrams which faithfully gives a diagrammatic representation of the structures of both the Heisenberg-Weyl algebra H - the associative algebra of the creation and annihilation operators of quantum mechanics - and U(L_H), the enveloping algebra of the Heisenberg Lie algebra L_H. We show explicitly how G may be endowed with the structure of a Hopf algebra, which is also mirrored in the structure of U(L_H). While both H and U(L_H) are images of G, the algebra G has a richer structure and therefore embodies a finer combinatorial realization of the creation-annihilation…
