Cummings Hamiltonian Research Articles

Quantum resonant optical bistability with a narrow atomic transition: bistability phase diagram in the bad cavity regime

We report on the observation of a novel manifestation of saturation-induced optical bistability in a resonantly pumped optical ring cavity interacting strongly with a cloud of atoms via a narrow atomic transition. The bistability emerges, above a critical pump rate, as an additional peak in the cavity’s normal mode spectrum close to atomic resonance. This third transmission peak is usually suppressed due to strong resonant absorption, but in our experiment it is visible because of the linewidth of the atomic transition being much smaller than that of the cavity, which sets the experiment into the bad-cavity regime. Relying on complete saturation of the transition, this bistability has a quantum origin and cannot be mimicked by a classical material presenting a nonlinear refraction index. The appearance of the central peak in addition to the normal modes is predicted by a semi-classical model derived from the Tavis–Cummings Hamiltonian from which we derive a bistability phase diagram that connects our observations with former work on optical bistability in the good cavity regime. The phase diagram reveals several so far unexplored bistable phases.

Time-Varying Engineered Reservoir for the Improved Estimation of Atom-Cavity Coupling Strength

In this paper, we consider the application of quantum reservoir engineering in quantum metrology. More precisely, we are concerned with a system setup where a sequence of atoms constructing the “time-varying” quantum reservoir interact, in turn, with the trapped field in a cavity through the Jaynes–Cummings Hamiltonian. In particular, we were able to manipulate the initial states of reservoir atoms in order to enhance estimation precision regarding the coupling strength between each atom and the cavity (the coupling strength between each atom and the cavity was assumed to be identical). The novelty of this work lies in alternately preparing the atoms at two different states in a pairwise manner, such that the cavity could converge into a squeezed state with photonic loss to the environment taken into account. The control scheme proposed here thus leads to higher precision compared to the previous work where reservoir atoms were initialized at the same state, which drove the cavity to a coherent state. Detailed theoretical analysis and numerical simulations are also provided. In addition, this system setup and the associated control scheme are easily implemented for quantum metrology, since no entanglement is required for the preparation of atom states, and the final cavity state can stay steady.

Exotic entanglement for non-Hermitian Jaynes–Cummings Hamiltonians

We provide the first solution of a time-dependent metric operator for the non-Hermitian Jaynes–Cummings Hamiltonian. We use this solution to calculate the entanglement between two identical isolated such Hamiltonians. The presence of a non-Hermitian interaction term leads to a spontaneously broken -symmetric regime which manifests itself in the exotic time-evolution of entanglement. When the symmetry is broken, oscillatory modes transition into decay. As such, there is a drastic difference in behaviour between the broken and unbroken regimes.

Approximate evolution for a system composed by two coupled Jaynes–Cummings Hamiltonians

In this work we construct an approximate time evolution operator for a system composed by two coupled Jaynes–Cummings Hamiltonians. We express the full time evolution operator as a product of exponentials and we analyze the validity of our approximations contrasting our analytical results with those obtained by purely numerical methods.

Non-Gaussian bosonic channels in the Tavis–Cummings model

The time evolution of two-level atoms interacting with a single-mode radiation field through the Tavis–Cummings Hamiltonian is studied from the perspective of channel action on the radiation mode. The operator sum representation for the channel in the situation of one atom interacting in resonance with the radiation mode, and two atoms interacting in resonance with the radiation mode, is obtained in the Fock basis. The notions of entanglement breaking, extremality, non-classicality and non-Gaussianity are explored using the obtained operator sum representation. It is shown that the respective channels are not entanglement breaking, are extremal and can generate both non-classicality and non-Gaussianity.

Ground state and thermal entanglement between two two-level atoms interacting with a nondegenerate parametric amplifier: Different sub-spaces

In this paper, a Hamiltonian model that includes interaction of two coupled two-level atoms with a nondegenerate parametric amplifier in a cavity is introduced. By using the two-mode squeezing operator and under a certain condition, the introduced Hamiltonian is reduced to a generalized Jaynes–Cummings Hamiltonian. The constants of motion of system imply the existence of a decomposition of the system’s Hilbert space [Formula: see text] into a direct sum of three infinite dimensional sub-spaces, as [Formula: see text]. This decomposition enables us to study ground and thermally induced entanglement between the atoms in each of the sub-spaces as well as whole Hilbert space. The effect of atom–atom and atom–photon couplings on the degree of ground state and thermal entanglement are also investigated using the concurrence measure. It is found that in the subspaces [Formula: see text] and [Formula: see text] for all experimental values of parameters of the system, the atoms are disentangled. It is also observed that in the total space [Formula: see text] the ground state entanglement is always zero, while in the subspace [Formula: see text] it is at its maximum value. Moreover, it is found that in the subspace [Formula: see text] thermal entanglement between the atoms is robust against temperature.

Novel transparency, absorption and amplification in a driven optomechanical system with a two-level defect

A study on optomechanically induced transparency (OMIT), optomechanically induced amplification (OMIAm) and optomechanically induced absorption (OMIAb) in a hybrid optomechanical system (OMS) with an intrinsic two-level defect was conducted. The OMS consists of a cavity, a mechanical resonator and a two-level defect. The coupling interaction between the two-level defect (the cavity field) and the mechanical resonator is described by the Jaynes–Cummings (radiation-pressure) Hamiltonian, while there is no direct coupling between the two-level defect and the cavity filed. In the resolved sideband regime, when only a probe light is applied on the left side of the cavity, double OMIT is obtained due to the additional interference pathway where spacing between the two transparency window dips is determined by the coupling strength between the two-level defect and the mechanical resonator. When an auxiliary driving field is applied on the mechanical resonator it induces OMIAm due to its negative impact on the cavity field. Further, with the increasing amplitude of the auxiliary driving field, amplitudes of the two transparency window dips symmetrically become much deeper. Moreover, when the two probe fields are applied to the right and left sides of the cavity, the destructive interference of the probe fields generates three channels of OMIAb, where summation of the excitations of resonator and two-level defect is always two times of the normalized intracavity probe photon number for different values of the effective radiation pressure coupling.

Self-oscillation in the Maxwell–Bloch equations

We elucidated the mechanism of supercritical Hopf bifurcation in the semi-classical Maxwell–Bloch equations for cavity quantum electrodynamics by formulating the atom–field interaction as a feedback control system. It turns out that the existence of self-oscillatory states is a rather unexpected manifestation of the atomic pseudospin precession dynamics born out of the atom–field interaction governed by the driven Jaynes–Cummings Hamiltonian.

Atom-field interaction in optical cavities: Calibration of the atomic velocities to obtain a list of field states with preselected properties

We investigate statistical properties of a single mode field that interacts with a two-level atom inside an optical cavity. The whole system is described by dispersive Jaynes–Cummings Hamiltonian, both subsystems starting from superpositions of two states. We consider properties of the field states only at the moment each atom is detected in the ground state immediately after it has crossed the cavity. This allows us to get a list of atomic velocities corresponding to field states with preselected properties. The scheme is exemplified for excitation inversion and sub-Poissonian statistics.

Modified n-level, n − 1-mode Tavis–Cummings model and algebraic Bethe ansatz

Using the quantum group technique we construct a one-parametric family of integrable modifications of the n-level, mode Tavis–Cummings Hamiltonian possessing an additional Stark-type term. We show that in the ‘quasiclassical’ limit the constructed Hamiltonian transforms into the integrable Hamiltonian of the quantum n-level, mode Tavis–Cummings model with the equal interaction strengths considered in Skrypnyk (2008 J. Phys. A: Math. Theor. 41 475202, 2009 J. Math. Phys. 50 103523). We diagonalize the constructed ‘modified’ Tavis–Cummings Hamiltonian and its second order integrals of motion using the nested Bethe ansatz.

Nonclassical properties of generalized four-photon coherent states

We proposed a scheme to generate new class of even(odd) compass states (specific superpositions of Wigner cat states [A. Dehghani et al., Ann. Phys. 362, 659 (2015)]), in the presence of the parity deformed Jaynes–Cummings Hamiltonian [A. Dehghani et al., Sci. Rep. 6, 38069 (2016)] describing a coupled system comprising a two-level atom and a cavity field assisted by a continuous external classical field. Particular attention was given to analyze their non-classical properties through of the Mandel’s parameter and quadrature squeezing. The Wigner compass states (WCSs) are compared with the ordinary ones, when the Wigner parameter becomes zero. Meanwhile generalized photon added compass states (PAWCSs) were introduced, by excitations of a newly introduced WCSs. Along with statistical analysis of latter case, a new theoretical framework for preparing them is suggested.

Protecting coherence by environmental decoherence: a solvable paradigmatic model

We consider a particularly simple exactly solvable model for a qubit coupled to sequentially nested environments. The purpose is to exemplify the coherence conserving effect of a central system, that has been reported as a result of increasing the coupling between near and far environment. The paradigmatic example is the Jaynes–Cummings Hamiltonian, which we introduce into a Kossakowski–Lindblad master equation using alternatively the lowering operator of the oscillator or its number operator as Lindblad operators. The harmonic oscillator is regarded as the near environment of the qubit, while effects of a far environment are accounted for by the two options for the dissipative part of the master equation. The exact solution allows us to cover the entire range of coupling strength from the perturbative regime to strong coupling analytically. The coherence conserving effect of the coupling to the far environment is confirmed throughout.

Effective spin physics in two-dimensional cavity QED arrays

We investigate a strongly correlated system of light and matter in two-dimensional cavity arrays. We formulate a multimode Tavis–Cummings (TC) Hamiltonian for two-level atoms coupled to cavity modes and driven by an external laser field which reduces to an effective spin Hamiltonian in the dispersive regime. In one-dimension we provide an exact analytical solution. In two-dimensions, we perform mean-field study and large scale quantum Monte Carlo simulations of both the TC and the effective spin models. We discuss the phase diagram and the parameter regime which gives rise to frustrated interactions between the spins. We provide a quantitative description of the phase transitions and correlation properties featured by the system and we discuss graph-theoretical properties of the ground states in terms of graph colourings using Pólya’s enumeration theorem.

Ionic vibration induced transparency and Autler–Townes splitting

In this work, the absorption spectrum of a two-level ion in a linear Paul trap is investigated, the ion is supposed to be driven by two orthogonal laser beams, the one along the axial of the trap acts as the control light beam, the other as probe beam. When the frequency of the control laser is tuned to the first red sideband of the ionic transition, the coupling between the internal states of the ion and vibrational mode turns out to be a Jaynes–Cummings (JC) Hamiltonian, which together with the coupling between the probe beam and the two-level ion constructs a -type three-level structure. In this case the transparency window may appear in the absorption spectrum of the probe light, which is induced by the ionic vibration and is very similar to the cavity induced transparency (Rice and Brecha 1996 Opt. Commun. 126 230–5). On the other hand, when the frequency of the control laser is tuned to the first blue sideband of the ionic transition, the two-level ion and vibrational mode are governed by an anti-Jaynes–Cummings (anti-JC) Hamiltonian, the total system including the probe beam forms a V-type three-level structure. And the Autler–Townes splitting in the absorption spectrum is found.

Upper bounded and sliced Jaynes– and anti-Jaynes–Cummings Hamiltonians and Liouvillians in cavity quantum electrodynamics

In this paper, we present a protocol to engineer upper bounded and sliced Jaynes–Cummings and anti-Jaynes–Cummings Hamiltonians in cavity quantum electrodynamics. In the upper bounded Hamiltonians, the atom-field interaction is confined to a subspace of Fock states ranging from up to , while in the sliced interaction the Fock subspace ranges from up to . We also show how to build upper bounded and sliced Liouvillians irrespective of engineering Hamiltonians. The upper bounded and sliced Hamiltonians and Liouvillians can be used, among other applications, to generate steady Fock states of a cavity mode and for the implementation of a quantum-scissors device for optical state truncation.

Generation of some entangled states of the cavity field

In this paper, we suggest a scheme which can produce various types of entangled states of the cavity field. In the scheme, cavities with different circumstances which evolve in time are utilized. It is shown that if two cavities are arranged in a way that, the first cavity is governed by the Jaynes---Cummings (JC) and the other with anti-Jaynes---Cummings (anti-JC) Hamiltonian, entangled EPR state of the cavity field is generated. Also, the proposal can be extended to the multi-cavity case, where the cavities are arranged such that their time evolutions change alternately from JC to anti-JC Hamiltonian. From this configuration, three- and four-partite GHZ states can be generated. At last, it is illustrated that in the multi-cavity set up if one prepares all cavities with the same time evolution property, $$W$$W state can be produced. An important feature of this scheme is the fact that the result of the processes is independent of the result of atomic detection.

A parafermionic generalization of the Jaynes–Cummings model

We introduce a parafermionic version of the Jaynes–Cummings Hamiltonian, by coupling k Fock parafermions (nilpotent of order F) to a 1D harmonic oscillator, representing the interaction with a single mode of the electromagnetic field. We argue that for k = 1 and F ⩽ 3 there is no difference between Fock parafermions and quantum spins . We also derive a semiclassical approximation of the canonical partition function of the model by assuming ℏ to be small in the regime of the large enough total number of excitations n, where the dimension of the Hilbert space of the problem becomes constant as a function of n. We observe in this case an interesting behaviour of the average of the bosonic number operator showing a single crossover between regimes with different integer values of this observable. These features persist when we generalize the parafermionic Hamiltonian by deforming the bosonic oscillator with a generic function Φ(x); the q-deformed bosonic oscillator corresponds to a specific choice of the deformation function Φ. In this particular case, we observe, at most k(F − 1), crossovers in the behaviour of the mean bosonic number operator, suggesting a phenomenology of superradiance similar to the k-atoms Jaynes–Cummings model.

Generation of W state and GHZ state of multiple atomic ensembles via a single atom in a nonresonant cavity

We propose a scheme for generation of the W state and the Greenberger–Horn–Zeilinger (GHZ) state of atomic ensembles. The scheme is based on the dynamics of a single control atom and atomic ensembles interacting with a nonresonant cavity mode. By choosing the appropriate parameters, the effective Hamiltonian describing the interaction between the control atom and the atomic modes shows complete analogy with the Jaynes–Cummings Hamiltonian. The required time for preparing the W state (GHZ state) keeps unchanged (increases linearly) with the increase of the number of atomic ensembles. The effects of dissipation and the detuning between the atomic modes and the control atom on the prepared states are analyzed by numerical simulation.

Phonon laser effect and Dicke–Hepp–Lieb superradiant phase transition in magnetic cantilever coupled to a Bose–Einstein condensate

We propose the possibility of a phonon laser by coupling a Bose–Einstein condensate to a nanomechanical cantilever with a magnetic tip. Due to the magnetic coupling, atomic spin flips induce cantilever motion, which can be used to produce a phonon laser. The system is described by the equivalent of the Jaynes–Cummings Hamiltonian. By controlling the number of atoms and the population inversion, one can obtain either a continuous wave or transient lasing. The two-body atom–atom interaction is also shown to coherently manipulate the lasing process. We also show that in the strong coupling limit, the same system can undergo a Dicke–Hepp–Lieb superradiant phase transition. Exotic phase diagrams can be obtained by tuning the two body atom–atom interaction.

ESTIMATION OF PURITY FOR A QUANTUM HARMONIC OSCILLATOR INITIALLY PREPARED IN A DISPLACED THERMAL STATE

We address the estimation of purity for a quantum oscillator initially prepared in a displaced thermal state and probed by a suitably prepared qubit interacting with the oscillator via Jaynes–Cummings Hamiltonian without the rotating-wave approximation. We evaluate the quantum Fisher information (QFI) and show that optimal estimation of purity can be achieved by measuring the population of the qubit after a properly chosen interaction time. We also address the estimation of purity at fixed total energy and show that the corresponding precision is independent of the presence of a coherent amplitude.