Adiabatic Elimination Research Articles

Dynamical phases of a Bose-Einstein condensate in a bad optical cavity at optomechanical resonance

We study the emergence of dynamical phases of a Bose-Einstein condensate that is optomechanically coupled to a dissipative cavity mode and transversally driven by a laser. We focus on the regime close to the optomechanical resonance, where the atoms' refractive index shifts the cavity into resonance, assuming fast cavity relaxation. We derive an effective model for the atomic motion, where the cavity degrees of freedom are eliminated using perturbation theory in the atom-cavity coupling and benchmark its predictions using numerical simulations based on the full model. Away from the optomechanical resonance, perturbation theory in the lowest order (adiabatic elimination) reliably describes the dynamics and predicts chaotic phases with unstable oscillations. Interestingly, the dynamics close to the optomechanical resonance are qualitatively captured only by including the corrections to next order (nonadiabatic corrections). In this regime we find limit-cycle phases that describe stable oscillations of the density with a well-defined frequency. We further show that such limit-cycle solutions are metastable configurations of the adiabatic model. Our work sheds light on the mechanisms that are required to observe dynamical phases and predict their existence in atom-cavity systems where a substantial timescale separation is present. Published by the American Physical Society 2025

Reconfiguration of Quantum Photonic Integrated Circuits Using Auxiliary Fields

AbstractManipulating photons in quantum photonic integrated circuits (QPICs) is essential for quantum communications and computation, demanding precise control over phase shifts and photon coupling. Despite the challenges arising from the low electro‐optic and thermo‐optic coefficients of glass waveguides, femtosecond laser direct writing (FsLDW) technology offers a rapid method for QPIC preparation. In this work, the use of auxiliary fields is proposed to reconfigure QPICs with FsLDW. Through adiabatic elimination, modulations of inter‐waveguide coupling are achieved, allowing for arbitrary, controllable beam‐splitting ratios and error correction in discrete quantum walking networks. The experiments also demonstrate full‐period phase shift modulation over 2π in a Mach‐Zehnder interferometer by employing an adjustable auxiliary field. Particularly, high‐quality two‐photon quantum interference and high‐fidelity quantum logic function conversion between a controlled‐NOT gate and a controlled‐PHASE gate are exhibited. This novel approach provides a promising mechanism for modulating the phase and coupling between photons in 3D and large‐scale QPICs.

Quantum state engineering in a five-state chainwise system by generalized coincident pulse technique.

In this paper, an exact analytical solution is presented for achieving coherent population transfer and creating arbitrary coherent superposition states in a five-state chainwise system by a train of coincident pulses. We show that the solution of a five-state chainwise system can be reduced to an equivalent three-state Λ-type one with the simplest resonant coupling under the assumption of adiabatic elimination together with a requirement of the relation among the four coincident pulses. In this method, the four coincident pulses at each step all have the same time dependence, but with specific magnitudes. The results show that, by using a train of appropriately coincident pulses, this technique not only enables complete population transfer, but also creates any desired coherent superposition between the initial and final states, while the population in all intermediate states is effectively suppressed. Furthermore, this technique can also exhibit a one-way population transfer behavior. The results are of potential interest in applications where high-fidelity multi-state quantum control is essential, e.g., quantum information, atom optics, formation of ultracold molecules, cavity QED, nuclear coherent population transfer, and light transfer in waveguide arrays.

Velocity selective multiple two-photon dark and bright resonances in Potassium vapor

We report the observation of two additional sub-natural line width quantum interferences in the D 2 manifold of 39 K vapor, in addition to the usual single Electromagnetically Induced Transparency (EIT) peak. In a typical three level Λ-type system, only one EIT peak is observed. However, here we report observation of two additional line shapes riding on top of the absorption profile. The fact that the hyperfine splitting is smaller than the Doppler width in 39 K allows the probe and control beams to swap their transition pathways in different velocity groups of atoms even when their frequencies are kept constant. Our observations are in striking contrast to standard EIT measurements. These findings are in quantitative agreement with density matrix formalism taking into account velocity-selective two-photon resonances. Owing to the favorably low ground hyperfine splitting (Δ hf ) in 39 K, which allows a significantly large number of atoms with a Doppler shift greater than or equal to the Δ hf , the strength of these additional resonances is strong compared to that of other alkali atoms such as 87 Rb, 133 Cs where these resonances can not be observed. The control photon detuning to atomic transition captures the nature of the coherence; therefore an unusual phenomenon of conversion from perfect transparency to enhanced absorption of the probe photon is observed and explained by utilizing the adiabatic elimination of the excited state in the Master equation. Controlling such dark and bright resonances leads to new applications in quantum technologies such as frequency-offset laser stabilization and long-lived quantum memory.

Spectral continuum in the Rabi–Stark model [Invited

The Rabi–Stark model is a nonlinear generalization of the quantum Rabi model including the dynamical Stark shift as a tunable term, which can be realized via quantum simulation on a cavity QED platform. When the Stark coupling becomes equal to the mode frequency, the spectrum changes drastically, a transition usually termed “spectral collapse” because numerical studies indicate an infinitely degenerate ground state. We show that the spectrum extends continuously from a threshold value up to infinity. A set of normalizable states is embedded in the continuum, which furnishes an unexpected analogy to the atomic Stark effect. Bound states and continuum can be obtained analytically through two equally justified but different confluence processes of the associated differential equation in Bargmann space. Moreover, these results are obtained independently using a method based on adiabatic elimination of the spin degree of freedom and corroborated through large-scale numerical checks.

Complete positivity violation of the reduced dynamics in higher-order quantum adiabatic elimination

Complete positivity violation of the reduced dynamics in higher-order quantum adiabatic elimination

Adiabatic elimination for composite open quantum systems: Reduced-model formulation and numerical simulations

Adiabatic elimination for composite open quantum systems: Reduced-model formulation and numerical simulations

Adiabatic elimination in the presence of multiphoton transitions in atoms inside a cavity

Various approaches have been used in the literature for eliminating nonresonant levels in atomic systems and deriving effective Hamiltonians. Important among these are elimination techniques at the level of probability amplitudes, operator techniques to project the dynamics on to the subspace of resonant levels, Green’s function techniques, the James’ effective Hamiltonian approach, etc. None of the previous approaches is suitable for deriving effective Hamiltonians in intracavity situations. However, the James’ approach does work in the case of only two-photon transitions in a cavity. A generalization of the James’ approach works in the case of three-photon transitions in a cavity, but only under Raman-like resonant conditions. Another important approach for adiabatic elimination is based on an adaptation of the Markov approximation well-known in the theory of system–bath interactions. However, this approach has not been shown to work in intracavity situations. In this paper, we present a method of adiabatic elimination for atoms inside cavities in the presence of multiphoton transitions. We work in the Heisenberg picture, and our approach has the advantage that it allows one to derive effective Hamiltonians even when Raman-like resonance conditions do not hold.

Stochastic resonance in Hindmarsh-Rose neural model driven by multiplicative and additive Gaussian noise

This paper investigates the occurrence of stochastic resonance in the three-dimensional Hindmarsh-Rose (HR) neural model driven by both multiplicative and additive Gaussian noise. Firstly, the three-dimensional HR neural model is transformed into the one-dimensional Langevin equation of the HR neural model using the adiabatic elimination method, and the effects of HR neural model parameters on the potential function are analyzed. Secondly the Steady-state Probability Density (SPD), the Mean First-Passage Time (MFPT), and the Signal-to-Noise Ratio (SNR) of the HR neural model are derived, based on two-state theory. Then, the effects of different parameters (a, b, c, s), noise intensity, and the signal amplitude on these metrics are analyzed through theoretical simulations, and the behavior of particles in a potential well is used to analyze how to choose the right parameters to achieve high-performance stochastic resonance. Finally, numerical simulations conducted with the fourth-order Runge–Kutta algorithm demonstrate the superiority of the HR neural model over the classical bistable stochastic resonance (CBSR) in terms of performance. The peak SNR of the HR neural model is 0.63 dB higher than that of the CBSR system. Simulation results indicate that the occurrence of stochastic resonance occur happens in HR neural model under different values of parameters. Furthermore, under certain conditions, there is a ‘suppress’ phenomenon that can be produced by changes in noise, which provides great feasibilities and practical value for engineering application.

Nonreciprocal optomechanically induced transparency and enhanced ground-state cooling in a reversed-dissipation cavity system.

We explore the prospects of phase-modulated optical nonreciprocity and enhanced ground-state cooling of a mechanical resonator for the reversed-dissipation system, where the dissipative coupling between two cavities is realized through the adiabatic elimination of a low-Q mechanical mode, while a high-Q mechanical mode interacts with two mutually coupled cavities, forming a closed-loop structure. This unique system facilitates the nontrivial phenomenon of optomechanically induced transparency (OMIT), which exhibits asymmetry due to the frequency shift effect. We also observe the emergence of parity-dependent unidirectional OMIT windows (appearing under the phase-matching condition), which can be dynamically modulated by both the phase factors and the strength of the dissipative coupling. Furthermore, our study delves into the ground-state cooling effect operating within the reversed-dissipation regime. Intriguingly, the cooling effect can be significantly enhanced by carefully engineering dissipative complex coupling, such as in the phase-matching condition. The potential applications of this scheme extend to the fabrication of ideal optical isolators in optical communication systems and the manipulation of macroscopic mechanical resonators at the quantum level, presenting exciting opportunities in quantum technologies.

Transition from traveling to motionless pulses in semiconductor lasers with saturable absorber

Transition from traveling to motionless pulses in semiconductor lasers with saturable absorber

Quantum Density Matrix Theory for a Laser Without Adiabatic Elimination of the Population Inversion: Transition to Lasing in the Class‐B Limit

Quantum Density Matrix Theory for a Laser Without Adiabatic Elimination of the Population Inversion: Transition to Lasing in the Class‐B Limit

Quantum control via chirped coherent anti-Stokes Raman spectroscopy

A chirped-pulse quantum control scheme applicable to coherent anti-Stokes Raman scattering spectroscopy, named as C-CARS, is presented aimed at maximizing the vibrational coherence in molecules. It implies chirping of three incoming pulses in the four-wave mixing process of CARS, the pump, the Stokes and the probe, to fulfill the conditions of adiabatic passage. The scheme is derived in the framework of rotating wave approximation and adiabatic elimination of excited state manifold simplifying the four-level model system into a ‘super-effective’ two level system. We demonstrate that the selectivity of excitation of vibrational degrees of freedom can be controlled by carefully choosing the spectral chirp rate of the pulses. The robustness, spectral selectivity and adiabatic nature of this method are advantageous for improving the existing methods of CARS spectroscopy for sensing, imaging and detection.

Effective dynamics and fluctuations of a trapped probe moving in a fluid of active hard discs (a)

We study the dynamics of a single trapped probe surrounded by self-propelled active particles in two dimensions. In the limit of large size separation, we perform an adiabatic elimination of the small active particles to obtain an effective Markovian dynamics of the large probe, yielding explicit expressions for the mobility and diffusion coefficient. To calculate these expressions, we perform computer simulations employing active Brownian discs and consider two scenarios: non-interacting bath particles and purely repulsive interactions modeling volume exclusion. We keep the probe-to-bath size ratio fixed and vary the propulsion speed of the bath particles. The positional fluctuations of a trapped probe are accessible in experiments, for which we test the prediction from the adiabatic elimination. We find that for a passive bath the Markovian prediction that the integrated force correlations equal the drag coefficient is not fulfilled in the simulations. However, this discrepancy is small compared to the active contribution and the overall agreement between predicted and measured probe fluctuations is very good at larger speeds.

Optical noise-resistant nonreciprocal phonon blockade in a spinning optomechanical resonator.

A scheme of nonreciprocal conventional phonon blockade (PB) is proposed in a spinning optomechanical resonator coupled with a two-level atom. The coherent coupling between the atom and breathing mode is mediated by the optical mode with a large detuning. Due to the Fizeau shift caused by the spinning resonator, the PB can be implemented in a nonreciprocal way. Specifically, when the spinning resonator is driven from one direction, the single-phonon (1PB) and two-phonon blockade (2PB) can be achieved by adjusting both the amplitude and frequency of the mechanical drive field, while phonon-induced tunneling (PIT) occurs when the spinning resonator is driven from the opposite direction. The PB effects are insensitive to cavity decay because of the adiabatic elimination of the optical mode, thus making the scheme more robust to the optical noise and still feasible even in a low-Q cavity. Our scheme provides a flexible method for engineering a unidirectional phonon source with external control, which is expected to be used as a chiral quantum device in quantum computing networks.

Nearly Hamiltonian dynamics of laser systems

The Arecchi-Bonifacio (or Maxwell-Bloch) model is the benchmark for the description of active optical media. However, in the presence of a fast relaxation of the atomic polarization, its implementation is a challenging task even in the simple ring-laser configuration, due to the presence of multiple timescales. In this paper we show that the dynamics is nearly Hamiltonian over timescales much longer than those of the cavity losses. More precisely, we prove that it can be represented as a pseudo spatiotemporal pattern generated by a nonlinear wave equation equipped with a Toda potential. The existence of two constants of motion (identified as pseudo energies), thereby elucidates the reason why it is so hard to simplify the original model: the adiabatic elimination of the polarization must be accurate enough to describe the dynamics correctly over unexpectedly long timescales. Finally, since the nonlinear wave equation with Toda potential can be simulated on much longer times than the previous models, this opens up the route to the numerical (and theoretical) investigation of realistic setups.

Behaviour and onset of low-dimensional chaos with a periodically varying loss in single-mode homogeneously broadened laser

Abstract In this work, we numerically study the behaviour of the single-mode homogeneously broadened laser versus a large perturbation of the steady state. Periodic behaviour develops for suitable values of the ratio of the population decay rates ℘ \wp , which has been analytically predicted by the analytical approach developed in the previous works, and for a pumping parameter 2 C 2C situated below and above the instability threshold 2 C 2 th 2{C}_{2{\rm{th}}} . We here show that the adiabatic elimination of the polarisation with sinusoidal time-dependent perturbation of the cavity rate leads the single-mode homogenously broadened laser to exhibit chaotic emission, if the frequency ω \omega is equal to the natural frequency Δ P {\Delta }_{P} . Increasing the pumping parameter 2 C 2C , the laser undergoes a period-doubling sequence. This cascade of period doubling drives the laser towards chaos. We also propose a reformulation of our analytical procedure, which describes the self-pulsing regime of the single-mode homogeneously broadened laser. We here report that asymmetric aspect that appears in the time evolution of the electric field is due to phase effects between the electric field components.

Coarse-Grained Effective Hamiltonian via the Magnus Expansion for a Three-Level System.

Quantum state processing is one of the main tools of quantum technologies. While real systems are complicated and/or may be driven by non-ideal control, they may nevertheless exhibit simple dynamics approximately confined to a low-energy Hilbert subspace. Adiabatic elimination is the simplest approximation scheme allowing us to derive in certain cases an effective Hamiltonian operating in a low-dimensional Hilbert subspace. However, these approximations may present ambiguities and difficulties, hindering a systematic improvement of their accuracy in larger and larger systems. Here, we use the Magnus expansion as a systematic tool to derive ambiguity-free effective Hamiltonians. We show that the validity of the approximations ultimately leverages only on a proper coarse-graining in time of the exact dynamics. We validate the accuracy of the obtained effective Hamiltonians with suitably tailored fidelities of quantum operations.

Adiabatic elimination theory of multi-level system in spin-orbit coupled Bose-Einstein condensate

In quantum optics, adiabatic elimination simplifies multi-level quantum system by eliminating the fast oscillatory degree of freedom and preserving the slow-varying dynamics, thus obtaining an efficient description of the system. Adiabatic elimination has important applications in quantum simulation and quantum precision measurement. For example, spin-orbit coupling has been realized in ultracold atoms by using three-level Raman coupling and adiabatic elimination. In this paper, we investigate the theoretical method and generalize the adiabatic elimination in three-level non-Hermitian systems and multi-level systems on the basis of standard elimination scheme. These can provide theoretical guidance for realizing the interdiscipline of non-Hermitian physics and spin-orbit coupling effects and their potential applications. We mainly discuss the influences of dissipative effect on the population dynamics of the system, the validity and accuracy of the adiabatic elimination theory under different parameters for both non-Hermitian and two types of five-level systems. Specifically, the dynamics satisfying the large detuning condition gives very accurate results for quite a long evolution time with the adiabatic elimination theory, but when the two-photon detuning <i>δ</i> and the Rabi frequency <inline-formula><tex-math id="Z-20231017181120">\begin{document}$\varOmega $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20231052_Z-20231017181120.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20231052_Z-20231017181120.png"/></alternatives></inline-formula> gradually increase, leading to the violation of the large detuning condition <inline-formula><tex-math id="M1">\begin{document}$ \varOmega,\gamma, \delta \ll \Delta$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20231052_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20231052_M1.png"/></alternatives></inline-formula>, the effective two-level model can no longer describe the fast-varying dynamics of the system even in a short evolution time. Thus the choice of system parameters affects the effectiveness of adiabatic elimination of the excited levels. In a non-Hermitian system, the population in the ground state oscillates with gain periodically at the beginning, while that in the ground state oscillates with loss and decreases with time, with the total population decreasing with oscillation. For long-time evolution the gain in the system causes the population to diverge, and the adiabatic elimination of the effective two-energy level system describes this behavior accurately. The effect of the non-Hermitian parameters on the dynamics of the system in the resonance case is manifested in the case that the total population remains conserved, while the total population tends to diverge for finite two-photon detuning. We find that with the increase of detuning, the divergence appears earlier and the total number of particles can be kept constant by choosing the ratio of gain to loss appropriately. This study provides a theoretical basis for state preparation and dynamical manipulation in dissipative multi-energy quantum systems.

Complete Positivity Violation in Higher-order Quantum Adiabatic Elimination

Complete Positivity Violation in Higher-order Quantum Adiabatic Elimination