arXiv subjects

Moein Malekakhlagh

Publications and source records attributed to Moein Malekakhlagh.

24 records · Page 2Linked to original sources

arXiv2019

Quantum Rabi Model with Two-Photon Relaxation

We study a cavity-QED setup consisting of a two-level system coupled to a single cavity mode with two-photon relaxation. The system dynamics is modeled via a Lindblad master equation consisting of the Rabi Hamiltonian and a two-photon dissipator. We show that an even-photon relaxation preserves the $Z_2$ symmetry of the Rabi model, and provide a framework to study the corresponding non-Hermitian dynamics in the number-parity basis. We discuss the role of different terms in the two-photon dissipator and show how one can extend existing results for the closed Rabi spectrum to the open case. Furthermore, we characterize the role of the $Z_2$ symmetry in the excitation-relaxation dynamics of the system as a function of light-matter coupling. Importantly, we observe that initial states with even-odd parity manifest qualitatively distinct transient and steady state behaviors, contrary to the Hermitian dynamics that is only sensitive to whether the initial state is parity-invariant. Moreover, the parity-sensitive dynamical behavior is not a creature of ultrastrong coupling and is present even at weak coupling values.

quant-ph↗

arXiv2017

Heisenberg-Langevin Formalism For Open Circuit-QED Systems

We present a Heisenberg-Langevin formalism to study the effective dynamics of a superconducting qubit coupled to an open multimode resonator, without resorting to the rotating wave, two level, Born or Markov approximations. Our effective equations are derived by eliminating resonator degrees of freedom while encoding their effect in the Green's function of the electromagnetic background. We account for the openness of the resonator exactly by employing a spectral representation for the Green's function in terms of a set of non-Hermitian modes. A well-behaved time domain perturbation theory is derived to systematically account for the nonlinearity of weakly nonlinear qubits like transmon. We apply this method to the problem of spontaneous emission, capturing accurately the non-Markovian features of the qubit dynamics, valid for any qubit-resonator coupling strength. Any discrete-level quantum system coupled to the electromagnetic continuum is subject to radiative decay and renormalization of its energy levels. When inside a cavity, these quantities can be strongly modified with respect to vacuum. Generally, this modification can be captured by including only the closest resonant cavity mode. In circuit-QED architecture, with substantial coupling strengths, it is however found that such rates are strongly influenced by far off-resonant modes. A multimode calculation over the infinite set of cavity modes leads to divergences unless an artificial cutoff is imposed. Previous studies have not pointed out what the source of this divergence is. We show that unless the effect of $A^2$ is accounted for up to all orders exactly, any multimode calculations of circuit-QED quantities is bound to diverge. Subsequently, we present the calculation of finite radiative corrections to qubit properties that is free of an artificially introduced high frequency cut-off.

quant-ph↗

arXiv2017

Cutoff-free Circuit Quantum Electrodynamics

Any quantum-confined electronic system coupled to the electromagnetic continuum is subject to radiative decay and renormalization of its energy levels. When coupled to a cavity, these quantities can be strongly modified with respect to their values in vacuum. Generally, this modification can be accurately captured by including only the closest resonant mode of the cavity. In the circuit quantum electrodynamics architecture, where the coupling strengths can be substantial, it is however found that the radiative decay rates are strongly influenced by far off-resonant modes. A multimode calculation accounting for the infinite set of cavity modes leads to divergences unless a cutoff is imposed. It has so far not been identified what the source of divergence is. We show here that unless gauge invariance is respected, any attempt at the calculation of circuit QED quantities is bound to diverge. We then present a theoretical approach to the calculation of a finite spontaneous emission rate and the Lamb shift that is free of cutoff.

quant-ph↗

arXiv2017

Non-Markovian dynamics of a superconducting qubit in an open multimode resonator

We study the dynamics of a transmon qubit that is capacitively coupled to an open multimode superconducting resonator. Our effective equations are derived by eliminating resonator degrees of freedom while encoding their effect in the Green's function of the electromagnetic background. We account for the dissipation of the resonator exactly by employing a spectral representation for the Green's function in terms of a set of non-Hermitian modes and show that it is possible to derive effective Heisenberg-Langevin equations without resorting to the rotating wave, two level or Markov approximations. A well-behaved time domain perturbation theory is derived to systematically account for the nonlinearity of the transmon. We apply this method to the problem of spontaneous emission, capturing accurately the non-Markovian features of the qubit dynamics, valid for any qubit-resonator coupling strength.

quant-ph↗

arXiv2015

Origin and Implications of $A^2$-like Contribution in the Quantization of Circuit-QED Systems

By placing an atom into a cavity, the electromagnetic mode structure of the cavity is modified. In Cavity QED, one manifestation of this phenomenon is the appearance of a gauge-dependent diamagnetic term, known as the $A^2$ contribution. Although in atomic Cavity QED, the resulting modification in the eigenmodes is negligible, in recent superconducting circuit realizations, such corrections can be observable and may have qualitative implications. We revisit the canonical quantization procedure of a circuit QED system consisting of a single superconducting transmon qubit coupled to a multimode superconducting microwave resonator. A complete derivation of the quantum Hamiltonian of an open circuit QED system consisting of a transmon qubit coupled to a leaky transmission line cavity is presented. We introduce a complete set of modes that properly conserves the current in the entire structure and present a sum rule for the dipole transition matrix elements of a multi-level transmon qubit coupled to a multi-mode cavity. Finally, an effective multi-mode Rabi model is derived with coefficients that are given in terms of circuit parameters.

cond-mat.mes-hall↗

arXiv2015

Beyond Strong Coupling in a Massively Multimode Cavity

The study of light-matter interaction has seen a resurgence in recent years, stimulated by highly controllable, precise, and modular experiments in cavity quantum electrodynamics (QED). The achievement of strong coupling, where the coupling between a single atom and fundamental cavity mode exceeds the decay rates, was a major milestone that opened the doors to a multitude of new investigations. Here we introduce multimode strong coupling (MMSC), where the coupling is comparable to the free spectral range (FSR) of the cavity, i.e. the rate at which a qubit can absorb a photon from the cavity is comparable to the round trip transit rate of a photon in the cavity. We realize, via the circuit QED architecture, the first experiment accessing the MMSC regime, and report remarkably widespread and structured resonance fluorescence, whose origin extends beyond cavity enhancement of sidebands. Our results capture complex multimode, multiphoton processes, and the emergence of ultranarrow linewidths. Beyond the novel phenomena presented here, MMSC opens a major new direction in the exploration of light-matter interactions.

quant-ph↗