The dissipative quantum Duffing oscillator: A comparison of Floquet-based approaches

Vierheilig, Carmen; Grifoni, Milena

doi:10.1016/j.chemphys.2010.06.023

Cited by 7 publications

(20 citation statements)

References 50 publications

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“…The results in Ref. [34] [33,34], the amplitude and phase are fully determined by knowledge of the matrix elements of the stationary density matrix of the Duffing oscillator in the Floquet basis [see, e.g., Eqs. (67)- (70) in Ref.…”

Section: Steady-state Dynamics Of a Duffing Oscillatormentioning

confidence: 99%

“…Here, we follow the same line of reasoning as in Ref. [34] to evaluate the amplitude and phase: we impose the same partial secular approximation and consider low temperatures k B T <h . However, we include now both emission and absorption processes; that is, we use the full dissipative transition rates as in Eq.…”

Section: Steady-state Dynamics Of a Duffing Oscillatormentioning

confidence: 99%

“…(67)- (70) in Ref. [34]]. There, the master equation yielding the elements of the stationary density matrix is analytically solved in the low-temperature regime k B T h imposing a partial secular approximation, yielding Eq.…”

Section: Steady-state Dynamics Of a Duffing Oscillatormentioning

confidence: 99%

“…(70) of Ref. [34], and restricting to spontaneous emission processes only. Here, we follow the same line of reasoning as in Ref.…”

Section: Steady-state Dynamics Of a Duffing Oscillatormentioning

confidence: 99%

“…These quantities were recently derived in Refs. [33,34], using the framework of a Bloch-Redfield-Floquet description of the dynamics of the DO. The results in Ref.…”

Section: Steady-state Dynamics Of a Duffing Oscillatormentioning

confidence: 99%

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Dynamics of a qubit coupled to a dissipative nonlinear quantum oscillator: An effective-bath approach

2011

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We consider a qubit coupled to a nonlinear quantum oscillator, the latter coupled to an Ohmic bath, and investigate the qubit dynamics. This composed system can be mapped onto that of a qubit coupled to an effective bath. An approximate mapping procedure to determine the spectral density of the effective bath is given. Specifically, within a linear response approximation the effective spectral density is given by knowledge of the linear susceptibility of the nonlinear quantum oscillator. To determine the actual form of the susceptibility, we consider its periodically driven counterpart, which is the problem of the quantum Duffing oscillator within linear response theory in the driving amplitude. Knowing the effective spectral density, the qubit dynamics is investigated. In particular, an analytic formula for the qubit's population difference is derived. Within the regime of validity of our theory, a very good agreement is found with predictions obtained from a Bloch-Redfield master equation approach applied to the composite qubit-nonlinear oscillator system.

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Section: Steady-state Dynamics Of a Duffing Oscillatormentioning

confidence: 99%

Section: Steady-state Dynamics Of a Duffing Oscillatormentioning

confidence: 99%

Section: Steady-state Dynamics Of a Duffing Oscillatormentioning

confidence: 99%

“…(70) of Ref. [34], and restricting to spontaneous emission processes only. Here, we follow the same line of reasoning as in Ref.…”

Section: Steady-state Dynamics Of a Duffing Oscillatormentioning

confidence: 99%

“…These quantities were recently derived in Refs. [33,34], using the framework of a Bloch-Redfield-Floquet description of the dynamics of the DO. The results in Ref.…”

Section: Steady-state Dynamics Of a Duffing Oscillatormentioning

confidence: 99%

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Dynamics of a qubit coupled to a dissipative nonlinear quantum oscillator: An effective-bath approach

2011

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Nonlinear spectroscopy of superconducting anharmonic resonators

DiVincenzo

Smolin²

2012

New J. Phys.

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We formulate a model for the steady state response of a nonlinear quantum oscillator structure, such as those used in a variety of superconducting qubit experiments, when excited by a steady, but not necessarily small, ac tone. We show that this model can be derived directly from a circuit description of some recent qubit experiments in which the state of the qubit is read out directly, without a SQUID magnetometer. The excitation profile has a rich structure depending on the detuning of the tone from the small-signal resonant frequency, on the degree of damping, and on the excitation amplitude. We explore two regions in detail: First, at high damping there is a trough in the excitation response as a function of detuning, near where the classical Duffing bifurcation occurs. This trough has been understood as a classical interference between two metastable responses with opposite phase. We use Wigner function studies to show that while this picture is roughly correct, there are also more quantum mechanical aspects to this feature. Second, at low damping we study the emergence of sharp, discrete spectral features from a continuum response. We show that these the structures, associated with discrete transitions between different excited-state eigenstates of the oscillator, provide an interesting example of a quantum Fano resonance. The trough in the Fano response evolves continuously from the "classical" trough at high damping.

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Quantum heating of a parametrically modulated oscillator: Spectral signatures

2011

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We show that the noise spectrum of a parametrically excited nonlinear oscillator can display a fine structure. It emerges from the interplay of the nonequidistance of the oscillator quasienergy levels and quantum heating that accompanies relaxation. The heating leads to a finite-width distribution over the quasienergy, or Floquet states even for zero temperature of the thermal reservoir coupled to the oscillator. The fine structure is due to transitions from different quasienergy levels, and thus it provides a sensitive tool for studying the distribution. For larger damping, where the fine structure is smeared out, quantum heating can be detected from the characteristic double-peak structure of the spectrum, which results from transitions accompanied by the increase or decrease of the quasienergy.

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The dissipative quantum Duffing oscillator: A comparison of Floquet-based approaches

Cited by 7 publications

References 50 publications

Dynamics of a qubit coupled to a dissipative nonlinear quantum oscillator: An effective-bath approach

Dynamics of a qubit coupled to a dissipative nonlinear quantum oscillator: An effective-bath approach

Nonlinear spectroscopy of superconducting anharmonic resonators

Quantum heating of a parametrically modulated oscillator: Spectral signatures

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