arXiv subjects

J. Talukdar

Publications and source records attributed to J. Talukdar.

4 recordsLinked to original sources

arXiv2024

Driven generalized quantum Rayleigh-van der Pol oscillators: Phase localization and spectral response

Driven classical self-sustained oscillators have been studied extensively in the context of synchronization. Using the master equation, this work considers the classically driven generalized quantum Rayleigh-van der Pol oscillator, which is characterized by linear dissipative gain and loss terms as well as three non-linear dissipative terms. Since two of the non-linear terms break the rotational phase space symmetry, the Wigner distribution of the quantum mechanical limit cycle state of the undriven system is, in general, not rotationally symmetric. The impact of the symmetry-breaking dissipators on the long-time dynamics of the driven system are analyzed as functions of the drive strength and detuning, covering the deep quantum to near-classical regimes. Phase localization and frequency entrainment, which are required for synchronization, are discussed in detail. We identify a large parameter space where the oscillators exhibit appreciable phase localization but only weak or no entrainment, indicating the absence of synchronization. Several observables are found to exhibit the analog of the celebrated classical Arnold tongue; in some cases, the Arnold tongue is found to be asymmetric with respect to vanishing detuning between the external drive and the natural oscillator frequency.

quant-ph↗

arXiv2023

Photon-induced droplet-like bound states in one-dimensional qubit array

We consider an array of $N_e$ non-interacting qubits or emitters that are coupled to a one-dimensional cavity array with tunneling energy $J$ and non-linearity of strength $U$. The number of cavities is assumed to be larger than the number of qubits. Working in the two-excitation manifold, we focus on the bandgap regime where the energy of two excited qubits is off-resonant with the two-photon bound state band. A two-step adiabatic elimination of the photonic degrees of freedom gives rise to a one-dimensional spin Hamiltonian with effective interactions; specifically, the Hamiltonian features constrained single-qubit hopping and pair hopping interactions not only between nearest neighbors but also between next-to-nearest and next-to-next-to-nearest spins. For a regularly arranged qubit array, we identify parameter combinations for which the system supports novel droplet-like bound states whose characteristics depend critically on the pair hopping. The droplet-like states can be probed dynamically. The bound states identified in our work for off-resonance conditions are distinct from localized hybridized states that emerge for on-resonance conditions.

quant-ph↗

arXiv2022

Two emitters coupled to a bath with Kerr-like non-linearity: Exponential decay, fractional populations, and Rabi oscillations

We consider two non-interacting two-level emitters that are coupled weakly to a one-dimensional non-linear wave guide. Due to the Kerr-like non-linearity, the wave guide considered supports -- in addition to the scattering continuum -- a two-body bound state. As such, the wave guide models a bath with non-trivial mode structure. Solving the time-dependent Schrödinger equation, the radiation dynamics of the two emitters, initially prepared in their excited states, is presented. Changing the emitter frequency such that the two-emitter energy is in resonance with one of the two-body bound states, radiation dynamics ranging from exponential decay to fractional populations to Rabi oscillations is observed. Along with the detuning, the dependence on the separation of the two emitters is investigated. Approximate reduced Hilbert space formulations, which result in effective emitter-separation and momentum dependent interactions, elucidate the underlying physical mechanisms and provide an avenue to showcase the features that would be absent if the one-dimensional wave guide did not contain a non-linearity. Our theoretical findings apply to a number of experimental platforms and the predictions can be tested with state-of-the-art technology. In addition, the weak-coupling Schrödinger equation based results provide critical guidance for the development of master equation approaches.

cond-mat.quant-gas↗

arXiv2022

Undamped Rabi oscillations due to polaron-emitter hybrid states in non-linear photonic wave guide coupled to emitters

The collective dynamics of two non-interacting two-level emitters, which are coupled to a structured wave guide that supports two-photon bound states, is investigated. Tuning the energy of the two emitters such that they are in resonance with the two-photon bound state energy band, we identify parameter regimes where the system displays fractional populations and essentially undamped Rabi oscillations. The Rabi oscillations, which have no analog in the single-emitter dynamics, are attributed to the existence of a collective polaron-like photonic state that is induced by the emitter-photon coupling. The full dynamics is reproduced by a two-state model, in which the photonic polaron interacts with the state $|e,e,\text{vac} \rangle$ (two emitters in their excited state and empty wave guide) through a Rabi coupling frequency that depends on the emitter separation. Our work demonstrates that emitter-photon coupling can lead to an all-to-all momentum space interaction between two-photon bound states and tunable non-Markovian dynamics, opening up a new direction for emitter arrays coupled to a waveguide.

cond-mat.quant-gas↗