Nonzero Detuning Research Articles

A Decoupled Feedback and Fast Norm Optimal Control approach for Normal and Superconducting RF Cavity disturbances compensation

Iterative learning controller (ILC)s of different types have been used in various engineering applications for system control in presence of repetitive disturbance, often encountered in batch control systems. A particle accelerator usually comprising of Radiofrequnecy (RF) cavities, when operated in pulsed mode processes particle beam similar to that in batch systems. However, an injected particle beam disturbs electric field inside RF cavity. In additions to beam loading disturbance encountered in all types of RF cavities, a superconducting cavity also encounters disturbance due to Lorentz force detuning. Under presence of such persisting disturbance/s, a Fast Norm Optimal ILC (FNOILC), helps achieve specified amplitude and phase stability of electric field, which results in beam of specified quality. A sophisticated control system helps achieve this objective. In this paper, FNOILC technique is explored for this purpose. Though, it has been reported for few accelerator facilities, in this work, a decoupling strategy is used in a feedback control loop, resulting into overall enhancement of control performance. Behavioral model of RF cavity is represented as dual input dual output system exhibiting two loops, found interacting due to nonzero cavity detuning. A decoupler is designed based on well known technique/s used in process control applications. Relative gain array element values are used to quantify interaction. In presence of beam loading disturbance, a FNOILC demonstrates an excellent control performance. A standard performance index has been used to assess control performance. It is found that use of decoupler in main feedback loop of RF cavity, enhances the resulting performance index. Besides, an ILC performance needs assessment with practical issues like model uncertainty, sensing delays, high detuning and observation noise. In this paper, most of conclusions are drawn based on large number of modeling and simulation studies carried out for lab prototype 650MHz cavity. Interesting studies like effects of low controller sampling frequency, feedback controller gain tuning, severe detuning, etc. are presented using a novel state plane representation. A zero phase filtering is simulated and proposed as an effective strategy when measurements have noise. This paper forms a case study which can be applied to any general system encountering repetitive disturbance. Additionally, paper also elaborates on FNOILC algorithm application for Lorentz force detuning compensation often encountered in superconducting cavity during pulse mode of operation.

Note on the emission spectrum and trapping states in the Jaynes–Cummings model

The emission of light from an atom represents a fundamental process that provides valuable insights into the atom–light interaction. The Jaynes–Cummings model is one of the simplest fully quantized models to deal with these interactions, allowing for an analytical solution, while exhibiting notable nontrivial effects. We explore new, to our knowledge, features in the fluorescence emission spectrum for initial “trapping states,” which suppress the atomic population inversion. Despite the seemingly dormant activity of the atom, the resulting emission spectra exhibit rich features, and using a dressed-state coordinates formalism, we are able to quantitatively explain the different profiles in the spectrum. We generalize the trapping conditions for nonzero atom-field detuning and also unveil two types of trapping states that lead to spectra with three peaks, in contrast to previously known states: a center peak and one secondary peak on each side. These are a trapping state formed by a Schrödinger cat state with Poissonian statistics (Yurke–Stoler state) and also a different type of “perfect trapping state.”

Tripartite entanglement in a detuned non-degenerate optical parametric oscillator

Continuous variable multipartite entanglement is an important resource in quantum optics and quantum information. Non-degenerate optical parametric oscillator (NOPO), generally working in a resonant regime, can generate high quality tripartite entanglement. However, the detuning in a real experiment is inevitable and sometimes necessary, for instance, in an optomechanical system. We calculate the tripartite entanglement from a detuned triply quasi-resonant NOPO. Unlike the previous literature using inseparability criterion, we use the positivity of partial transpose, a sufficient and necessary criterion, to characterize the tripartite entanglement with full inseparability generated from a detuned NOPO. We also consider the influence of the pump and signal/idler losses on the tripartite entanglement. The results show that, the tripartite entanglement could exist even with a large detuning of several times cavity linewidth, and may be better for a detuned regime than for the resonant one under some conditions. With a fixed non-zero loss which always exists in a real experiment, an appropriate value of non-zero detuning could lead to the best entanglement. What’s more, unlike the bipartite entanglement, which exists both below and above threshold, the tripartite entanglement only occurs for a nonzero classical amplitude of signal/idler field. The jumping between the tripartite and bipartite entanglement could make the NOPO become a quantum state switch element, which promises a potential application on the multiparty quantum secret sharing.

Energy transport induced by transition from the weak to the strong coupling regime between non-Hermitian optical systems

The strong coupling between non-Hermitian physical systems of different natures has been widely investigated recently since it endows them with new properties. In this work, we consider energy transport through an open quantum optical system consisting of strongly coupled subsystems. We use a partial-secular approach for the description of an open quantum system to investigate the system dynamics during the transition from a weak to a strong coupling regime with an increase of coupling between subsystems. On the example of strongly coupled two-level atoms, we show that during the transition to the strong coupling regime, the enhancement of energy transport through the open quantum system takes place. Namely, starting from zero value, when the coupling constant equals zero, the stationary energy flow increases and tends to an approximately constant value at the high values of the coupling constant. As a result, the specific energy flow—the stationary energy flow normalized to the coupling constant—reaches the maximum at some value of the coupling constant. This behavior takes place even in the case of the non-zero frequency detuning when there is no clear transition point from the weak to the strong coupling regime in the spectrum of system eigenvalues. Thus, to achieve significant energy flow through the compound open quantum system, it is sufficient to restrict the value of the coupling constant at which the specific energy flow is maximized. Also, we demonstrate the suppression of the stationary energy flow at high dissipation rates. The obtained results can be used in the design of quantum thermal devices.

Two ground-state bright solitons in fractional-order spin–orbit-coupled Bose–Einstein condensates

We study two types of bright solitons in zero and non-zero detuning spin–orbit-coupled (SOC) Bose–Einstein condensates in fractional effect by variational and imaginary-time evolution method. The results show that the variation of SOC with fractional kinetic energy operator affects the existence and form of solitons. In particular, we found that SOC strength could be a transition point. In other words, for and , the soliton states and pseudo-spin polarization in non-zero detuning show opposite changes. In addition, moving bright solitons with zero and non-zero detuning are studied.

Robust two-state swap by stimulated Raman adiabatic passage

Efficient initialization and manipulation of quantum states is important for numerous applications and it usually requires the ability to perform high fidelity and robust swapping of the populations of quantum states. Stimulated Raman adiabatic passage (STIRAP) has been known to perform efficient and robust inversion of the ground states populations of a three-level system. However, its performance is sensitive to the initial state of the system. In this contribution we demonstrate that a slight modification of STIRAP, where we introduce a non-zero single-photon detuning, allows for efficient and robust population swapping for any initial state. The results of our work could be useful for efficient and robust state preparation, dynamical decoupling and design of quantum gates in ground state qubits via two-photon interactions.

Bell-inequality violation by dynamical Casimir photons in a superconducting microwave circuit

We study the Bell's inequality violation by dynamical Casimir radiation with pseudospin measurement. We consider a circuit quantum electrodynamical set-up where a relativistically moving mirror is simulated by variable external magnetic flux in a SQUID terminating a superconducting-microwave waveguide. We analytically obtain expectation values of the Bell operator optimized with respect to channel orientations, in terms of the system parameters. We consider the effects of local noise in the microwave field modes, asymmetry between the field modes resulting from nonzero detuning, and signal loss. Our analysis provides ranges of the above experimental parameters for which Bell violation can be observed. We show that Bell violation can be observed in this set-up up to 40 mK temperature as well as up to 65 % signal loss.

Quantum Interstate Phase Differences and Multiphoton Processes: Quantum Jumps or Dynamic Beats?

Whether quantum state transitions occur by instantaneous jumps (a la Bohr) or deterministic dynamics (Schrödinger’s preference) has been intensely debated. Recent experimental measurements of shelved electrons have reignited the debate. We examine aspects of the time-dependent numerical solutions of the Schrödinger equation in quantum systems with two and three levels perturbed by a sinusoidal field. A geometrical construction involving quantum state phase differences illuminates the role of interstate phase differences in a deterministic, rather than random, process of multiphoton absorption. Alternate halves of the Rabi cycle exhibit phase reversals much like the classical beats of coupled oscillators. For non-zero detuning, population inversion does not occur because the exciting field drifts out of the proper phase before inversion is complete. A close correspondence with classical, coupled oscillator beats offers insights for interpretation of deterministic quantum dynamics and suggests an experimental test for the correctness of this picture depending on the long-time phase stability of exciting fields.

Homodyne coherent quantum noise cancellation in a hybrid optomechanical force sensor

In this paper we propose an experimentally viable scheme to enhance the sensitivity of force detection in a hybrid optomechanical setup assisted by squeezed vacuum injection, beyond the standard quantum limit (SQL). The scheme is based on a combination of the coherent quantum noise cancellation (CQNC) strategy with a variational homodyne detection of the cavity output spectrum in which the phase of the local oscillator is optimized. In CQNC, realizing a negative-mass oscillator in the system leads to exact cancellation of the backaction noise from the mechanics due to destructive quantum interference. Squeezed vacuum injection enhances this cancellation and allows sub-SQL sensitivity to be reached in a wide frequency band and at much lower input laser powers. We show here that the adoption of variational homodyne readout enables us to enhance this noise cancellation up to $40\phantom{\rule{3.33333pt}{0ex}}\mathrm{dB}$ compared to the standard case of detection of the optical output phase quadrature, leading to a remarkable force sensitivity of the order of ${10}^{\ensuremath{-}19}\phantom{\rule{0.28em}{0ex}}\mathrm{N}/\sqrt{\mathrm{Hz}}$, about $70%$ enhancement compared to the standard case. Moreover, we show that at nonzero cavity detuning, the signal response can be amplified at a level three to five times larger than that in the standard case without variational homodyne readout, improving the signal-to-noise ratio. Finally, the variational readout CQNC developed in this paper may be applied to other optomechanical-like platforms such as levitated systems and multimode optomechanical arrays or crystals as well as Josephson-based optomechanical systems.

Asymptotic Entanglement Sudden Death in Two Atoms with Dipole-Dipole and Ising Interactions Coupled to a Radiation Field at Non-Zero Detuning.

We investigate the time evolution and asymptotic behavior of a system of two two-level atoms (qubits) interacting off-resonance with a single mode radiation field. The two atoms are coupled to each other through dipole–dipole as well as Ising interactions. An exact analytic solution for the system dynamics that spans the entire phase space is provided. We focus on initial states that cause the system to evolve to entanglement sudden death (ESD) between the two atoms. We find that combining the Ising and dipole–dipole interactions is very powerful in controlling the entanglement dynamics and ESD compared with either one of them separately. Their effects on eliminating ESD may add up constructively or destructively depending on the type of Ising interaction (Ferromagnetic or anti-Ferromagnetic), the detuning parameter value, and the initial state of the system. The asymptotic behavior of the ESD is found to depend substantially on the initial state of the system, where ESD can be entirely eliminated by tuning the system parameters except in the case of an initial correlated Bell state. Interestingly, the entanglement, atomic population and quantum correlation between the two atoms and the field synchronize and reach asymptotically quasi-steady dynamic states. Each one of them ends up as a continuous irregular oscillation, where the collapse periods vanish, with a limited amplitude and an approximately constant mean value that depend on the initial state and the system parameters choice. This indicates an asymptotic continuous exchange of energy (and strong quantum correlation) between the atoms and the field takes place, accompanied by diminished ESD for these chosen setups of the system. This system can be realized in spin states of quantum dots or Rydberg atoms in optical cavities, and superconducting or hybrid qubits in linear resonators.

Fine structure of second-harmonic resonances in χ(2) optical microresonators.

Owing to the discrete frequency spectrum of whispering gallery resonators (WGRs), the resonance and phase-matching conditions for the interacting waves in the case of second-harmonic generation (SHG) cannot generally be fulfilled simultaneously. To account for this, we develop a model describing SHG in WGRs with non-zero frequency detunings at both the pump and second-harmonic frequencies. Our model predicts strong distortions of the line shape of pump and second-harmonic resonances for similar linewidths at both frequencies; for much larger linewidths at the second-harmonic frequency, this behavior is absent. Furthermore, it describes the SHG efficiency as a function of detuning. Experimentally, one can change the WGR eigenfrequencies, and thus the relative detuning between pump and second-harmonic waves by a number of means, for example electro-optically and thermally. Using a lithium niobate WGR, we show an excellent quantitative agreement for the SHG efficiency between our experimental results and the model. Also, we show the predicted distortions of the pump and second-harmonic resonances to be absent in the lithium niobate WGR but present in a cadmium silicon phosphide WGR, as expected from the linewidths of the resonances involved.

Optimal dispersive readout of a spin qubit with a microwave resonator

Strong coupling of semiconductor spin qubits to superconducting microwave resonators was recently demonstrated. These breakthroughs pave the way for quantum information processing that combines the long coherence times of solid-state spin qubits with the long-distance connectivity, fast control, and fast high-fidelity quantum-non-demolition readout of existing superconducting qubit implementations. Here, we theoretically analyze and optimize the dispersive readout of a single spin in a semiconductor double quantum dot (DQD) coupled to a microwave resonator via its electric dipole moment. The strong spin-photon coupling arises from the motion of the electron spin in a local magnetic field gradient. We calculate the signal-to-noise ratio (SNR) of the readout accounting for both Purcell spin relaxation and spin relaxation arising from intrinsic electric noise within the semiconductor. We express the maximum achievable SNR in terms of the cooperativity associated with these two dissipation processes. We find that while the cooperativity increases with the strength of the dipole coupling between the DQD and the resonator, it does not depend on the strength of the magnetic field gradient. We then optimize the SNR as a function of experimentally tunable DQD parameters. We identify wide regions of parameter space where the unwanted backaction of the resonator photons on the qubit is small. Moreover, we find that the coupling of the resonator to other DQD transitions can enhance the SNR by at least a factor of two, a ``straddling'' effect that occurs only at nonzero energy detuning of the DQD double-well potential. We estimate that with current technology, single-shot readout fidelities in the range $82-95\%$ can be achieved within a few $\mu\textrm{s}$ of readout time without requiring the use of Purcell filters.

Manipulating entanglement sudden death in two coupled two-level atoms interacting off-resonance with a radiation field: an exact treatment.

We study a model of two coupled two-level atoms (qubits) interacting off-resonance (at non-zero detuning) with a single mode radiation field. This system is of special interest in the field of quantum information processing (QIP) and can be realized in electron spin states in quantum dots or Rydberg atoms in optical cavities and superconducting qubits in linear resonators. We present an exact analytical solution for the time evolution of the system starting from any initial state. Utilizing this solution, we show how the entanglement sudden death (ESD), which represents a major threat to QIP, can be efficiently controlled by tuning atom-atom coupling and non-zero detuning. We demonstrate that while one of these two system parameters may not separately affect the ESD, combining the two can be very effective, as in the case of an initial correlated Bell state. However in other cases, such as a W-like initial state, they may have a competing impacts on ESD. Moreover, their combined effect can be used to create ESD in the system, as in the case of an anti-correlated initial Bell state. A clear synchronization between the population inversion collapse-revival pattern and the entanglement dynamics is observed at all system parameter combinations. Nevertheless, only for initial states that may evolve to ESD, the population inversion revival oscillations, where exchange of energy between the atoms and the field takes place, temporally coincide with the entanglement revival peaks, whereas the population collapse periods match the ESD intervals. The variation of the radiation field intensity has a clear impact on the duration of the ESD at any combination of the other system parameters.

Optimal estimation of matter-field coupling strength in the dipole approximation

This paper is devoted to the study of the Bayesian-inference approach in the context of estimating the dipole coupling strength in matter-field interactions. In particular, we consider the simplest model of a two-level system interacting with a single mode of the radiation field. Our estimation strategy is based on the emerging state of the two-level system, whereas we determine both the minimum mean-square error and maximum likelihood estimators for uniform and Gaussian prior probability density functions. In the case of the maximum likelihood estimator, we develop a mathematical method which extends the already existing approaches to the variational problem of the average cost function. We demonstrate that long interaction times, large initial mean photon numbers, and nonzero detuning between two-level system transition and the frequency of the electromagnetic field mode have a deleterious effect on the optimality of the estimation scenario. We also present several cases where the estimation process is inconclusive, despite many ideal conditions being met.

Exceptional points in two dissimilar coupled diode lasers

We show the abundance of exceptional points in the generic asymmetric configuration of two coupled diode lasers, under nonzero optical detuning and differential pumping. We pinpoint the location of these points with respect to the stability domains and the Hopf bifurcation points of phase-locked modes, in the solution space as well as in the space of experimentally controlled parameters.

Gap solitons in spin–orbit-coupled Bose–Einstein condensates in bichromatic optical lattices

We investigate gap solitons in spin–orbit-coupled Bose–Einstein condensates in bichromatic optical lattices and mainly focus the effect of the secondary periodic potential trap on the gap solitons. The gap solitons and linear Bloch waves are obtained by solving coupled Gross–Pitaevskii equations in bichromatic optical lattice. The results show that parity symmetry plays an important role when the detuning between the Raman beam and energy levels of the atoms is zero. It is shown that the soliton amplitude increases with the increasing secondary periodic potential well depth. The gap solitons become spin polarization for the case of nonzero detuning. Linear stability analysis method has been employed to investigate the stability of gap solitons located in the first and second band gaps. The results prove that the periodic secondary potential trap depths have important effects on the stability of gap solitons.

CUSP-SINGULARITY OF THE TRAJECTORY OF THE QUBIT’S BLOCH VECTOR UNDER AN EXTERNAL PERIODIC LIGHT FIELD

The quantum dynamics of a two-level quantum-mechanical system subjected to the external monochromatic action beyond the rotating wave approximation was investigated. It was shown that under the condition of exact resonance on the trajectories of the Bloch vectors, special points are manifested under different initial conditions. These points are classified as cusps singularities. It is revealed that at such points, the instantaneous rotation axis, relative to which the Bloch vector rotates, reverses its direction. There is a movement stop. For a nonzero frequency detuning, the cusp singularities vanish. A numerical analysis of the singularities of the trajectories of the Bloch vector without rotating wave approximation was supplemented by a study based on the use of the Floquet methods. Within the framework of this approach, recurrence relations for the spectral components of the probability amplitudes were obtained and analyzed. An analytic expression was found for the two values of quasi-energies within a fourth order of magnitude in the interaction energy. It was shown that to obtain a singular behavior of the trajectories of the Bloch vector, it is sufficient to confine by four spectral harmonics in the Floquet expansion. The results obtained are important for achieving the accuracy when performing coherent transformations with two-level systems in the cases where the rotating wave approximation is inapplicable.

Two types of ground-state bright solitons in a coupled harmonically trapped pseudo-spin polarization Bose–Einstein condensate**Project supported by the National Natural Science Foundation of China (Grant Nos. 11304270 and 11475144).

We study two types of bright solitons in an attractive Bose–Einstein condensate with a spin–orbit interaction. By solving the coupled nonlinear Schrödinger equations with the variational method and the imaginary time evolution method, fundamental properties of solitons are carefully investigated in different parameter regimes. It is shown that the detuning between the Raman beam and energy states of the atoms dominates the ground state type and spin polarization strength. The soliton dynamics is also studied for various moving velocities for zero and nonzero detuning cases. We find that the shape of individual component solitons can be maintained when the moving speed of solitons is low and the detuning is small in the coupled harmonically trapped pseudo-spin polarization Bose–Einstein condensate.

Quantum revivals of a non-Rabi type in a Jaynes–Cummings model

We studied full revivals of quantum states in the Jaynes-Cannings model. It is proved that in the case of zero detuning in subspaces generated by two adjacent pairs of energy levels, full revival of the subspace does not exist for any values of the parameters. In the case of non-zero detuning on the contrary, the set of parameters that allows full revival of such subspaces is dense as the subset of all parameters. The nature of these revivals differs from Rabi oscillations in subspaces of a single pair of energy. In more complex subspaces the presence of full revival is reduced to particular cases of 10-th Hilbert problem for rational solutions of systems of nonlinear algebraic equations, which has no algorithmic solution in general case.

Correlation spectroscopy in cold atoms: Light sideband resonances in electromagnetically-induced-transparency condition

The correlation spectroscopy has been successfully employed in the measurement of the intrinsic linewidth of electromagnetically induced transparency (EIT) in time and frequency domain. We study the role of the sidebands of the intense fields in the measured spectra, analyzing the information that can be recovered working with different analysis frequencies. In this case, the nonzero one-photon detuning appears as a necessary condition for spectrally resolving the sideband resonances in the correlation coefficient. Our experimental findings are supported by the perturbative model defined in the frequency domain.