Noise in a superconducting single-electron transistor resonator driven by an external field

Rodrigues, D. A.; Milburn, G. J.

doi:10.1103/physrevb.78.104302

Cited by 3 publications

(8 citation statements)

References 38 publications

(119 reference statements)

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“…In a limit-cycle, the effective damping can be generalized to obtain an amplitude dependent damping 1,3,15,33 γ eff (E) where E ≈ n is the average energy. The calculation, which is described in Ref.…”

Section: Origin Of the Peak Widthsmentioning

confidence: 99%

“…The calculation, which is described in Ref. 33, proceeds by deriving a set of Langevin equations for the SSET and resonator operators. Assuming then that the resonator energy relaxes much more slowly than the SSET charge, the problem can be separated into two parts (though at the cost of neglecting some of the SSET-resonator correlations).…”

Section: Origin Of the Peak Widthsmentioning

confidence: 99%

“…The driven charge response as a function of the resonator amplitude is then used to obtain an effective Langevin equation for the resonator alone. 33 Writing down the corresponding equation for the average amplitude of the resonator leads immediately to the effective damping, an expression for which (valid in the limit E J ≪ Γ) is given in the appendix. The average energy of the resonator obeys the equation of motion,…”

Section: Origin Of the Peak Widthsmentioning

confidence: 99%

“…The same approach also allows us to calculate the renormalized frequency of the resonator, Ω R (as we discuss in the appendix). The calculation of γ eff (E) requires 15,33 approximations in which certain correlations between the resonator and the SSET are dropped. Not surprisingly, this approach does not capture all of the coupled dynamics of the system and in particular it does not describe the small shift in the SSET frequency which arises due to the coupling to the resonator.…”

Section: Origin Of the Peak Widthsmentioning

confidence: 99%

“…Mapping the effective Langevin equation for the resonator 33 onto a c-number equation, 35 we then follow the approach of Lax, 23,34 and derive effective equations of motion for the phase and amplitude. The calculation follows very closely that described in Ref.…”

Section: Origin Of the Peak Widthsmentioning

confidence: 99%

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Spectral properties of a resonator driven by a superconducting single-electron transistor

2010

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We analyze the spectral properties of a resonator coupled to a superconducting single-electron transistor ͑SSET͒ close to the Josephson quasiparticle resonance. Focusing on the regime where the resonator is driven into a limit-cycle state by the SSET, we investigate the behavior of the resonator linewidth and the energy relaxation rate which control the widths of the main features in the resonator spectra. We find that the linewidth becomes very narrow in the limit-cycle regime, where it is dominated by a slow phase-diffusion process, as in a laser. The overall phase-diffusion rate is determined by a combination of direct phase diffusion and the effect of amplitude fluctuations which affect the phase because the resonator frequency is amplitude dependent. For sufficiently strong couplings we find that a regime emerges where the phase diffusion is no longer minimized when the average resonator energy is maximized. Finally we show that the current noise of the SSET provides a way of measuring both the linewidth and energy relaxation rate.

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Section: Origin Of the Peak Widthsmentioning

confidence: 99%

Section: Origin Of the Peak Widthsmentioning

confidence: 99%

Section: Origin Of the Peak Widthsmentioning

confidence: 99%

Section: Origin Of the Peak Widthsmentioning

confidence: 99%

Section: Origin Of the Peak Widthsmentioning

confidence: 99%

See 3 more Smart Citations

Spectral properties of a resonator driven by a superconducting single-electron transistor

2010

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Lattice properties ofPbX(X=S,Se,Te
Romero
¹
,
Cardona
²
,
Kremer
³

et al. 2008
Phys. Rev. B
61
7
39
1
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During the past five years the low temperature heat capacity of simple semiconductors and insulators has received renewed attention. Of particular interest has been its dependence on isotopic masses and the effect of spin-orbit coupling in ab initio calculations. Here we concentrate on the lead chalcogenides PbS, PbSe and PbTe. These materials, with rock salt structure, have different natural isotopes for both cations and anions, a fact that allows a systematic experimental and theoretical study of isotopic effects e.g. on the specific heat. Also, the large spin-orbit splitting of the 6p electrons of Pb and the 5p of Te allows, using a computer code which includes spin-orbit interaction, an investigation of the effect of this interaction on the phonon dispersion relations and the temperature dependence of the specific heat and on the lattice parameter. It is shown that agreement between measurements and calculations significantly improves when spin-orbit interaction is included.

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Fano-Like Antiresonances in Nanomechanical and Optomechanical Systems

Rodrigues

2009

Phys. Rev. Lett.

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We study a resonator coupled to a generic detector and calculate the noise spectra of the two sub-systems. We describe the coupled system by a closed, linear, set of Langevin equations and derive a general form for the finite frequency noise of both the resonator and the detector. The resonator spectrum is the well-known thermal form with an effective damping, frequency shift and diffusion term. In contrast, the detector noise shows a rather striking Fano-like resonance, i.e. there is a resonance at the renormalized frequency, and an anti-resonance at the bare resonator frequency. As examples of this effect, we calculate the spectrum of a normal state single electron transistor coupled capacitively to a resonator and of a cavity coupled parametrically to a resonator. PACS numbers: 85.85.+j, 85.35.Gv, 42.79.Gn When a mechanical resonator is coupled to a detector, even weakly, the detector can have a significant effect on the dynamics of the resonator, and it is this "backaction" that ultimately enforces the standard quantum limit of measurement [1]. For weak enough coupling, the detector acts like an additional thermal bath, providing an effective frequency shift, damping and temperature. This effective temperature can be lower than that of the resonator's environment, so a detector, such as an optical/microwave cavity or a mesoscopic conductor, can cool the resonator [2, 3], potentially to its ground state ([4] and refs. therein). Linear response theory gives a general way of calculating the noise spectrum of a resonator coupled to a detector, which is found to be very close to a thermal spectrum [5]. A relevant question is if a thermal model is enough to fully capture the dynamics of the system, or if there are any effects beyond a purely thermal back action. In particular, when calculating the spectrum of the detector, can we still treat the back action as purely thermal?In this Letter, we consider a detector linearly coupled to a resonator, and calculate the noise spectrum of both. As expected, the resonator spectrum is essentially thermal, with the frequency, damping and temperature modified by the back-action. We might therefore expect that the detector spectrum is close to the spectrum of a backaction-free detector coupled to a resonator with this modified thermal bath. However, we find that this is not the case, and show that the noise in the detector instead has a rather striking feature akin to a Fano resonance [6], i.e. a resonance at the renormalized resonator frequency plus an anti-resonance at the original frequency. Fano resonances arise from the interference between coherent and incoherent paths in mesoscopic conductors [7], but resonance/anti-resonance pairs are a general interference phenomenon, occurring in systems from LC circuits to electromagnetically induced transparency (EIT) [8,9].We first outline our general formalism before deriving an expression for the spectrum of a generic detector coupled to a resonator. Finally, we illustrate the analysis with two examples: a single electron tr...

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Noise in a superconducting single-electron transistor resonator driven by an external field

Cited by 3 publications

References 38 publications

Spectral properties of a resonator driven by a superconducting single-electron transistor

Spectral properties of a resonator driven by a superconducting single-electron transistor

Lattice properties ofPbX(X=S,Se,Te
Romero
¹
,
Cardona
²
,
Kremer
³

et al. 2008
Phys. Rev. B
61
7
39
1
View full text Add to dashboard Cite

Fano-Like Antiresonances in Nanomechanical and Optomechanical Systems

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Noise in a superconducting single-electron transistor resonator driven by an external field

Cited by 3 publications

References 38 publications

Spectral properties of a resonator driven by a superconducting single-electron transistor

Spectral properties of a resonator driven by a superconducting single-electron transistor

Lattice properties ofPbX(X=S,Se,TeRomero1, Cardona2, Kremer3 et al. 2008Phys. Rev. B617391View full textAdd to dashboardCite

Fano-Like Antiresonances in Nanomechanical and Optomechanical Systems

Contact Info

Product

Resources

About

Lattice properties ofPbX(X=S,Se,Te
Romero
¹
,
Cardona
²
,
Kremer
³

et al. 2008
Phys. Rev. B
61
7
39
1
View full text Add to dashboard Cite