Macroscopic quantum effects in a strongly driven nanomechanical resonator

Peano, Vittorio; Thorwart, Michael

doi:10.1103/physrevb.70.235401

Cited by 62 publications

(102 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Several experimental groups have observed the behavior described by the classical Duffing oscillator [27,28,29,30]. The transition to the quantum regime is currently in the focus of intense research [31,32,33,34,35,36]. Once, such kind of truly quantum-'mechanical' systems on the nanoscale have been shown to exist, macroscopic quantum effects [33] should be readily observable.…”

Section: Discussionmentioning

confidence: 99%

“…The transition to the quantum regime is currently in the focus of intense research [31,32,33,34,35,36]. Once, such kind of truly quantum-'mechanical' systems on the nanoscale have been shown to exist, macroscopic quantum effects [33] should be readily observable. A second class of experimental systems addresses the resonant non-destructive read-out of a persistent current qubit [37,38,39,40].…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamics of the quantum Duffing oscillator in the driving induced bistable regime

Peano

Thorwart

2006

Chemical Physics

Self Cite

View full text Add to dashboard Cite

We investigate the nonlinear response of an anharmonic monostable quantum mechanical resonator to strong external periodic driving. The driving thereby induces an effective bistability in which resonant tunneling can be identified. Within the framework of a Floquet analysis, an effective Floquet-Born-Markovian master equation with time-independent coefficients can be established which can be solved straightforwardly. Various effects including resonant tunneling and multi-photon transitions will be described. Our model finds applications in nano-electromechanical devices such as vibrating suspended nano-wires as well as in non-destructive readout procedures for superconducting quantum bits involving the nonlinear response of the read-out SQUID.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Dynamics of the quantum Duffing oscillator in the driving induced bistable regime

Peano

Thorwart

2006

Chemical Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…We find a characteristic asymmetry of the antiresonance lineshape. In contrast to [20,21,22,23], our analytic results are obtained without applying a rotating wave approximation (RWA) on the Duffing oscillator. The paper is organized as follows: In section 2 we introduce the Hamiltonian of the non-dissipative Duffing oscillator and the two Floquet based approximation schemes to treat it.…”

Section: Introductionmentioning

confidence: 99%

“…In particular Rigo et al [19] demonstrated, based on a quantum diffusion model, that in the steady state the quantum DO does not exhibit any bistability or hysteresis. It was also shown that the response of the Duffing oscillator displays antiresonant dips and resonant peaks [20,21,22,23] depending on the frequency of the driving field, originating from special degeneracies of the eigenenergy spectrum of the nonlinear oscillator [20]. While the antiresonances persist in the presence of a weak Ohmic bath, for strong damping the nonlinear response turns to a resonant behaviour, namely the one of a linear oscillator at a shifted frequency [22].…”

Section: Introductionmentioning

confidence: 99%

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

Vierheilig¹,

Grifoni²

2010

Chemical Physics

View full text Add to dashboard Cite

We study the dissipative quantum Duffing oscillator in the deep quantum regime with two different approaches: The first is based on the exact Floquet states of the linear oscillator and the nonlinearity is treated perturbatively. It well describes the nonlinear oscillator dynamics away from resonance. The second, in contrast, is applicable at and in the vicinity of a N-photon resonance and it exploits quasi-degenerate perturbation theory for the nonlinear oscillator in Floquet space. It is perturbative both in driving and nonlinearity. A combination of both approaches yields the possibility to cover the whole range of driving frequencies. As an example we discuss the dissipative dynamics of the Duffing oscillator near and at the one-photon resonance.

show abstract

“…Most of the features of Josephson bifurcation amplifiers, in fact, only rely on (and can consequently be described by) any type of nonlinearity [17][18][19][20][21][22] , e.g., Duffing-type models, so that only recently the full nonlinear potential of the JJ has become of interest in this field 23 .…”

Section: Introductionmentioning

confidence: 99%

Resonators coupled to voltage-biased Josephson junctions: From linear response to strongly driven nonlinear oscillations

et al. 2015

View full text Add to dashboard Cite

Motivated by recent experiments, where a voltage biased Josephson junction is placed in series with a resonator, the classical dynamics of the circuit is studied in various domains of parameter space. This problem can be mapped onto the dissipative motion of a single degree of freedom in a nonlinear time-dependent potential, where in contrast to conventional settings the nonlinearity appears in the driving while the static potential is purely harmonic. For long times the system approaches steady states which are analyzed in the underdamped regime over the full range of driving parameters including the fundamental resonance as well as higher and sub-harmonics. Observables such as the dc-Josephson current and the radiated microwave power give direct information about the underlying dynamics covering phenomena as bifurcations, irregular motion, up-and down conversion. Due to their tunability, present and future set-ups provide versatile platforms to explore the changeover from linear response to strongly nonlinear behavior in driven dissipative systems under well defined conditions. I. INTRODUCTIONThe nonlinear properties of Josephson junctions (JJs) have made such devices a key circuit element for classical and quantum electronics. Accordingly, there has been a long tradition of studying non-linear phenomena in driven superconducting circuits, starting as early as the 1960s with the discovery of Shapiro steps 1 . While Shapiro-steps have remained a tool in exploring new directions in Josephson physics, for instance in atomic point contacts 2-6 , other nonlinear phenomena, like synchronization, have been investigated in arrays of JJs: as a test-bed for generic theory models to capture synchronization phenomena 7,8 , but as importantly with the prospect of applications as sources of more intense coherent radiation 9 , cf. also new developments using intrinsic arrays 10-12 .More recently, the nonlinearity of the JJ was exploited as the crucial factor in enabling the high sensitivity of Josephson bifurcation amplifiers, achieving substantial improvements towards reaching quantum-limited measurement processes [13][14][15][16] . Most of the features of Josephson bifurcation amplifiers, in fact, only rely on (and can consequently be described by) any type of nonlinearity 17-22 , e.g., Duffing-type models, so that only recently the full nonlinear potential of the JJ has become of interest in this field 23 .A recent addition to the field of driven nonlinear JJs 24-26 are experiments on a dc-biased JJ connected to a resonator 27-29 . In this sort of setup, charge transfer through the JJ leads to excitations in the resonator, and therefore allows to convert energy carried by charge quanta into quantum microwave photons. In these devices measurement of both the Josephson current and the emitted microwave radiation is possible, a distinct advantage in comparison to other recently proposed transport setups 30,31 , which show similar nonlinear features like bifurcations, period multiplication and up-and downconversion 32-34 . S...

show abstract

Macroscopic quantum effects in a strongly driven nanomechanical resonator

Cited by 62 publications

References 33 publications

Dynamics of the quantum Duffing oscillator in the driving induced bistable regime

Dynamics of the quantum Duffing oscillator in the driving induced bistable regime

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

Resonators coupled to voltage-biased Josephson junctions: From linear response to strongly driven nonlinear oscillations

Contact Info

Product

Resources

About