Using a qubit to measure photon-number statistics of a driven thermal oscillator

Abstract

We demonstrate theoretically how photon-number statistics of a driven damped oscillator at finite temperature can be extracted by measuring the dephasing spectrum of a two-level system dispersively coupled to the oscillator; we thus extend the work of M. I. Dykman and M. A. Krivoglaz ͓Sov. Phys. Solid State 29, 210 ͑1987͔͒ and J. Gambetta et al. ͓Phys. Rev. A 74, 042318 ͑2006͔͒. We carefully consider the fidelity of this scheme-to what extent does the measurement reflect the initial number statistics of the mode? We also derive analytic results for the dephasing of a qubit by a driven thermal mode, and compare results obtained at different levels of approximation. Our results have relevance both to experiments in circuit cavity QED, as well as to nanoelectromechanical systems.

Photon Statistics of Propagating Thermal Microwaves

“…Here, γ 1 (n r ) is the total qubit relaxation rate and γ ϕ0 is the qubit dephasing rate due to all other noise sources except for those described by C(τ ). Assuming δϕ 2 /2 = γ ϕn (n r )τ and |χ| κ x , the photon-field-induced dephasing rates approximate to [25,41,49,[55][56][57] γ th ϕn (n r ) =κ x θ 2 0 (n 2 r + n r )≡ s th 0 (n 2 r + n r ) ,…”

“…These emitters can be spatially separated from the setup components used for manipulation and detection [18,19], which allows one to individually control the emitter and the setup temperature. Due to the low energy of microwave photons, the detection of these fields typically requires the use of nearquantum-limited amplifiers [20][21][22][23], cross-correlation detectors [17, 18, 24], or superconducting qubits [25][26][27][28].The unique nature of propagating fields is reflected in their photon statistics, which is described by a probability distribution either in terms of the number states or in terms of its moments. The former were studied by coupling the field to an atom or qubit and measuring the coherent dynamics [29][30][31] or by spectroscopic analysis [32].…”

“…These emitters can be spatially separated from the setup components used for manipulation and detection [18,19], which allows one to individually control the emitter and the setup temperature. Due to the low energy of microwave photons, the detection of these fields typically requires the use of nearquantum-limited amplifiers [20][21][22][23], cross-correlation detectors [17, 18, 24], or superconducting qubits [25][26][27][28].…”

Macrorealism inequality for optoelectromechanical systems

“…In this new picture, the QND measurement scheme proposed and analyzed elsewhere 25,28,39 applies for a large bias…”

Nanomechanical-resonator-assisted induced transparency in a Cooper-pair box system

“…Currently, there are experimental and theoretical groups devoted to observing quantum effects in truly solid-state mechanical oscillators or cantilever systems [1]- [21]. In the regime when the individual mechanical quanta are of the order of or greater than the thermal energy, quantum effects become important and the motion of the mechanical resonator or cantilever is close to or on the verge of the quantum limit.…”