Rotating Wave Approximation Research Articles

Highly non-resonant lasing without inversion gain in a ladder scheme

We show that it is possible to get gain without inversion at high frequency in a three-level ladder type scheme driven by a single driving laser. The transition from the ground state to first excited state is driven by a low-frequency resonant laser field. The next excited state lies far above the first one; therefore its resonant frequency can be much higher than that of the lower transition, and hence one should go beyond the most commonly used rotating wave approximation consisting of retaining only resonant terms (slowly oscillating) in the Hamiltonian. We solve the master equation, both analytically (under proper approximations) and numerically, with the full Hamiltonian keeping counter-rotating highly non-resonant terms. We show a dressed state picture explaining spectral features of gain-absorption profiles. Also we present a kind of phase diagram in the plane γ–Λ, where γ and Λ are spontaneous emission rate and incoherent pumping rate, respectively. The whole γ–Λ plane is divided into four areas: gain-inversion, absorption-no inversion, gain without inversion and absorption with inversion. The first two are usual regimes of incoherently pumped lasers, while the last two stem from the quantum interference phenomena. We analyse the parameter areas where such quantum regimes are possible. The exact numerical solution of the time-dependent master equation shows that keeping counter-rotating terms (no rotating wave approximation) gives rise to new spectral features in the form of additional peaks at combination frequencies. Actually the considered system works as a coherent frequency up-converter.

Radiation-induced interaction potential of two qubits strongly coupled with a quantized electromagnetic field

We investigate the interaction of two two-level qubits with a single mode quantum field in a cavity without rotating wave approximation and considering that qubits can be located at an arbitrary distance from each other. We demonstrate that there exists a radiation induced interaction potential between atoms. We studied the properties of the system numerically and in addition constructed a simple analytical approximation. It is shown that the observable characteristics are substantially dependent on the distance between the qubits in the strong coupling regime. This allows one to perform the quantum control of the qubits, which can be exploited for the recording and transmission of quantum information.

Optomechanical cooling by STIRAP-assisted energy transfer: an alternative route towards the mechanical ground state

Standard optomechanical cooling methods ideally require weak coupling and cavity damping rates which enable the motional sidebands to be well resolved. If the coupling is too large then sideband-resolved cooling is unstable or the rotating wave approximation can become invalid. In this work we describe a protocol to cool a mechanical resonator coupled to a driven optical mode in an optomechanical cavity, which is also coupled to an optical mode in another auxiliary optical cavity, and both the cavities are frequency-modulated. We show that by modulating the amplitude of the drive as well, one can execute a type of STIRAP transfer of occupation from the mechanical mode to the lossy auxiliary optical mode which results in cooling of the mechanical mode. We show how this protocol can outperform normal optomechanical sideband cooling in various regimes such as the strong coupling and the unresolved sideband limit.

Jaynes-Cummings model under monochromatic driving

We study analytically and numerically the properties of Jaynes-Cummings model under monochromatic driving. The analytical results allow to understand the regime of two branches of multi-photon excitation in the case of close resonance between resonator and driven frequencies. The rotating wave approximation allows to reduce the description of original driven model to an effective Jaynes-Cummings model with strong coupling between photons and qubit. The analytical results are in a good agreement with the numerical ones even if there are certain deviations between the theory and numerics in the close vicinity of the resonance. We argue that the rich properties of driven Jaynes-Cummings model represent a new area for experimental investigations with superconducting qubits and other systems.

Quantum parameter estimation in a dissipative environment

We investigate the performance of quantum parameter estimation based on a qubit probe in a dissipative bosonic environment beyond the traditional paradigm of weak-coupling and rotating-wave approximations. By making use of an exactly numerical hierarchical equations of motion method, we analyze the influences of the non-Markovian memory effect induced by the environment and the form of probe-environment interaction on the estimation precision. It is found that (i) the non-Markovianity can effectively boost the estimation performance and (ii) the estimation precision can be improved by introducing a perpendicular probe-environment interaction. Our results indicate the scheme of parameter estimation in a noisy environment can be optimized via engineering the decoherence mechanism.

Monoatomic chain: modulational instability and exact traveling wave solutions

The objective of this work is to study a monoatomic chain which is described by the Klein–Gordon model with first and second neighbors anharmonic interactions. We consider specifically the case where both of these interactions are of cubic–quartic type and show, through the rotating wave approximation, that envelop waves in our model are governed by a modified nonlinear Schrodinger equation. The modulational instability is investigated on the latter, with a particular attention on the impact of the second neighbors. It is then revealed that the second neighbors interaction increases the regions of instability in the space of parameters and, hence, expands the possibility of propagating solitary waves in the network. More importantly, we derive the exact solutions of our modified nonlinear Schrodinger equation and show the influence of the second neighbors on them. For example, the width of these solutions can be controlled by adjusting the parameters relative to the second neighbors. Numerical simulations are done in order to confirm the analytical studies. Equally, the methods used in this study can also be implemented on other nonlinear equations.

Parity-to-charge conversion in Majorana qubit readout

We study the time-dependent effect of Markovian readout processes on Majorana qubits whose parity degrees of freedom are converted into the charge of a tunnel-coupled quantum dot. By applying a recently established effective Lindbladian approximation [1-3], we obtain a completely positive and trace preserving Lindblad master equation for the combined dot-qubit dynamics, describing relaxation and decoherence processes beyond the rotating-wave approximation. This approach is applicable to a wide range of weakly coupled environments representing experimentally relevant readout devices. We study in detail the case of thermal decay in the presence of a generic Ohmic bosonic bath, in particular for potential fluctuations in an electromagnetic circuit. In addition, we consider the nonequilibrium measurement environment for a parity readout using a quantum point contact capacitively coupled to the dot charge.

Entrainment of Weakly Coupled Canonical Oscillators with Applications in Gradient Frequency Neural Networks Using Approximating Analytical Methods

Solving phase equations for systems with high degrees of nonlinearities is cumbersome. However, in the case of two coupled canonical oscillators, that is, a reduced model of translated Wilson–Cowan neuronal dynamics, under slowly varying amplitude and rotating wave approximations, we suggested a convenient way to find their average relative phase evolution. This approach enabled us to find an explicit solution for the average relative phase of the two coupled canonical oscillators based on the original neuronal model parameters, and importantly, to find their phase-locking constraint. This methodology is straightforward to implement in any Wilson–Cowan-type coupled oscillators with applications in gradient frequency neural networks (GFNNs).

Bound states in ultrastrong waveguide QED

We discuss the properties of bound states in finite-bandwidth waveguide QED beyond the Rotating Wave Approximation or excitation number conserving light-matter coupling models. Therefore, we extend the \emph{standard} calculations to a broader range of light-matter strengths, in particular, in the so-called ultrastrong coupling regime. We do this using the Polaron technique. Our main results are as follows. We compute the spontaneous emission rate, which is renormalized as compared to the Fermi Golden Rule formula. We generalise the existence criteria for bound states, their properties and their role in the qubits thermalization. We discuss effective spin-spin interactions through both vacuum fluctuations and bound states. Finally, we sketch a perfect state-transfer protocol among distant emitters.

High Gain Coefficient Parametric Amplification of Optical Phonon Mode in Magnetized AIIIBV Semiconductor Plasmas

Using the hydrodynamic (fluid) model of plasmas, we have studied the threshold and gain characteristics of parametric amplification of optical phonon mode in magnetized AIIIBV semiconductor plasmas. The origin of nonlinear interaction is assumed to lie in second-order nonlinearity arising due to nonlinear coupling of pump wave, optical phonon and signal modes in the medium. Theoretical formulation has been carried out with the help of coupled mode theory under rotating-wave approximation. Numerical estimates have been made for a representative magnetized doped AIIIBV semiconductor crystal (viz. n-InSb) irradiated by a pulsed 10.6 μm CO2 laser. The analysis enables us to choose one of the three achievable resonance conditions: (electron–cyclotron frequency ~ pump frequency, coupled cyclotron– plasmon frequency ~ Stokes frequency, coupled cyclotron–plasmon frequency ~ optical phonon frequency), at which threshold pump amplitude reduces, whereas parametric gain coefficient enhances nearly hundred times. The lowering of threshold and enhancement of parametric gain coefficient, in AIIIBV semiconductors under proper selection of doping concentration and externally applied magnetic field, confirm the chosen nonlinear medium as a potential candidate material for fabrication of optical parametric amplifier with enhanced gain coefficient.

Diagrammatic approach for analytical non-Markovian time evolution: Fermi's two-atom problem and causality in waveguide quantum electrodynamics

Non-Markovian time evolution of quantum systems is a challenging problem, often mitigated by employing numerical methods or making simplifying assumptions. In this work, we address this problem in waveguide quantum electrodynamics (QED) by developing a diagrammatic approach, which performs fully analytical non-Markovian time evolution of single-photon states. By revisiting Fermi's two-atom problem, we tackle the impeding question of whether the rotating-wave approximation violates causality in single-photon waveguide QED. Afterward, we introduce and prove the no upper half-plane poles (no-UHP) theorem, which connects the poles of scattering parameters to the causality principle. Finally, we visualize the time-delayed coherent quantum feedback mediated by the field and discuss the Markovian limit for microscopically separated qubits where short-distance causality violations occur and the emergence of collective decay rates in this limit. Our diagrammatic approach is a method to perform exact and analytical non-Markovian time evolution of multiemitter systems in waveguide QED.

Deep strong light-matter coupling in plasmonic nanoparticle crystals.

In the regime of deep strong light-matter coupling, the coupling strength exceeds the transition energies of the material1-3, fundamentally changing its properties4,5; for example, the ground state of the system contains virtual photons and the internal electromagnetic field gets redistributed by photon self-interaction1,6. So far, no electronic excitation of a material has shown such strong coupling to free-space photons. Here we show that three-dimensional crystals of plasmonic nanoparticles can realize deep strong coupling under ambient conditions, if the particles are ten times larger than the interparticle gaps. The experimental Rabi frequencies (1.9 to 3.3 electronvolts) of face-centred cubic crystals of gold nanoparticles with diameters between 25 and 60 nanometres exceed their plasmon energy by up to 180 per cent. We show that the continuum of photons and plasmons hybridizes into polaritons that violate the rotating-wave approximation. The coupling leads to a breakdown of the Purcell effect-the increase of radiative damping through light-matter coupling-and increases the radiative polariton lifetime. The results indicate that metallic and semiconducting nanoparticles can be used as building blocks for an entire class of materials with extreme light-matter interaction, which will find application in nonlinear optics, the search for cooperative effects and ground states, polariton chemistry and quantum technology4,5.

Floquet spectrum and electronic transitions of tilted anisotropic Dirac materials under electromagnetic radiation: Monodromy matrix approach

We analyze the quasienergy-spectrum and the valence to conduction-band transition probabilities of a tilted anisotropic Dirac material subject to linearly and circularly polarized electromagnetic fields. The quasienergy-spectrum is numerically calculated from the monodromy matrix of the Schr\"odinger equation via the Floquet theorem for arbitrarily intense electromagnetic fields. To asses the valence to conduction-band transition times we deduced a Rabi-like formula in the rotating wave approximation. In the strong-field regime the spectrum as a function of the momentum components divides into two very distinctive regions. In the first, located around the Dirac point, the quasi-spectrum is significantly distorted by the field as the electronic parameters are renormalized by electronic-dressing. In the second, all the characteristics of the free carrier spectrum are retained. Linearly polarized light anisotropically deforms the spectrum according to the field polarization direction. Dirac-like points form around the original Dirac point. The quasi spectrum of circularly polarized light, instead, exhibits a gap formation in the Dirac point and has elliptical symmetry. We show that, in contrast to the single-photon resonant transitions that characterize the weak-field regime, the strong-field regime is dominated by multiphoton resonances.

Sub-Poissonian statistics and squeezing of magnons due to the Kerr effect in a hybrid coupled cavity–magnon system

We investigate theoretically the quantum dynamics and statistics of magnons in a cavity–magnon system, where the magnons in a single yttrium iron garnet (YIG) sphere are coupled to microwave cavity photons. Under the rotating wave approximation, the Hamiltonian of the system is solved analytically. By using the coherent magnon state representation, we show that the magnon Kerr nonlinearity, which originates in the magnetocrystalline anisotropy in the YIG sample, could yield a periodic sub-Poissonian distribution and quadrature squeezing effects in the magnons. The generation and manipulation of these nonclassical quantum statistical properties of the magnons can be controlled by scaling the size of the YIG sample.

Dissipative Rabi model in the dispersive regime

The dispersive regime of circuit QED is the main workhorse for todays quantum computing prototypes based on superconducting qubits. Analytic descriptions of this model typically rely on the rotating wave approximation of the interaction between the qubits and resonators, using the Jaynes-Cummings model as starting point for the dispersive transformation. Here we present analytic results on the dispersive regime of the dissipative Rabi model, without taking the rotating wave approximation of the underlying Hamiltonian. Using a recently developed hybrid perturbation theory based on the expansion of the time evolution on the Keldysh contour [Phys. Rev. A 95, 013847 (2017)], we derive simple analytic expressions for all experimentally relevant dynamical parameters like dispersive shift and resonator induced Purcell decay rate, focussing our analysis on a generic multi-level qubit. The analytical equations are easily tractable and reduce to the known Jaynes-Cummings results in the relevant limit. They however show qualitative differences at intermediate and large detuning, allowing for more accurate modelling of the interaction between superconducting qubits and resonators. In the limit of strong resonator driving, our results additionally predict new types of drive induced qubit dissipation and dephasing, not present in previous theories.

Dynamics of a periodic XY chain coupled to a photon mode

We study the real-time dynamics of a periodic $XY$ system exposed to a composite field comprised of a constant homogeneous magnetic and a quantized circularly polarized electromagnetic fields. The interaction between the quantized mode and spin-magnetic moments is modeled by the Dicke Hamiltonian. The rotating wave approximation is applied and the conditions for its validity are discussed. It is shown that if initially all of the excitations are contained in the field, then in the regime of large detuning, the main evolutionary effect involves oscillations of the excitations between the zero-momentum modes of the chain and the field. Accordingly, the reduced photon number and magnetization per site reveal a sort of oscillatory behavior. Effective Hamiltonians describing the short-time dynamics of the present model for small number of excitations and large detuning are introduced. The resonance case is considered in the context of photon emission from the chain initially prepared in the (partially) excited state. In particular, it is demonstrated, in the framework of a specific example, that the superradiant behavior shows up at the beginning of the emission, when we have an initial state with a maximally excited $XY$ chain. Possible applications of the model to problems such as spin chain and $J$-aggregate in a single-mode cavity are discussed.

Nonlinear optical absorption coefficient and refractive index change in symmetric semiconductor nanostructures: Comparison between different methods

Abstract We present a systematic study of the optical absorption coefficient (OAC) and refractive index change (RIC) for a symmetric semiconductor nanostructure. We derived the OAC and RIC following two approaches, one without approximations, besides the usual ones (rotating-wave approximation and application of a two-level model), and the other using an approximation keeping only the contribution of the linear and third-order nonlinear terms. In the derivation we consider properly the contribution of the population decay time and the dephasing time, which may be different to each other, in general, in semiconductor nanostructures, extending previous works. We also apply the derived formulae for the calculation of the OAC and RIC in a specific semiconductor quantum well with position-dependent mass and compared the results obtained from the derived formulae. We find that while for low light intensities the different formulae for OAC and RIC give similar results for higher light intensities only the formulae obtained without approximations can lead to correct physical results. We also present a critical intensity below which the different formulae for OAC and RIC give practically the same results. This critical intensity can be used for obtaining correct behavior for the OAC and RIC in any symmetric semiconductor nanostructure.

Effective pulse reverse-engineering for strong field-matter interaction.

In this Letter, we propose a scheme to control the evolution of a two-level quantum system in the strong-coupling regime, based on the idea of reverse engineering. A coherent control field is designed to drive the system along a user-predefined evolution trajectory without utilizing the rotating-wave approximation. As concrete examples, we show that complete population inversion, an equally weighted coherent superposition, and even oscillation-like dynamics can be achieved. Since there are no limitations on the coupling strength between the control field and matter, the scheme is attractive for applications such as accelerating desired system dynamics and fast quantum information processing.

Quantum control via enhanced shortcuts to adiabaticity

Fast and robust quantum control protocols are often based on an idealised approximate description of the relevant quantum system. While this may provide a performance which is close to optimal, improvements can be made by incorporating elements of the full system representation. We propose a new technique for such scenarios, called enhanced shortcuts to adiabaticity (eSTA). The eSTA method works for previously intractable Hamiltonians by providing an analytical correction to existing STA protocols. This correction can be easily calculated and the resulting protocols are outside the class of STA schemes. We demonstrate the effectiveness of the method for three distinct cases: manipulation of an internal atomic state beyond the rotating wave approximation, transport of a neutral atom in an optical Gaussian trap and transport of two trapped ions in an anharmonic trap.

Evanescent Wave Approximation for Non-Hermitian Hamiltonians.

The counterpart of the rotating wave approximation for non-Hermitian Hamiltonians is considered, which allows for the derivation of a suitable effective Hamiltonian for systems with some states undergoing decay. In the limit of very high decay rates, on the basis of this effective description we can predict the occurrence of a quantum Zeno dynamics, which is interpreted as the removal of some coupling terms and the vanishing of an operatorial pseudo-Lamb shift.