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Physical review. B, Condensed matter

Detection of quantum noise

Uri Gavish, Yehoshua B. Levinson, Y. Imry

Published Oct 15, 2000• 168 citations
Publisher

Abstract

We discuss the detection of quantum fluctuations in the light of the relationship between time-dependent correlators and measurable properties [L. Van Hove, Phys. Rev 95, 249 (1954)]. Considering the interaction between the fluctuating electron system and a resonant circuit or a photon mode, we prove that zero-point fluctuations (ZPF) are not observable by a passive detector, corroborating the results of Lesovik and Loosen (Pis'ma Zh. \'Eksp. Teor. Fiz. [JETP Lett. 65, 269 (1997)]). By a passive detector we mean one which is itself effectively in the ground state, and cannot transfer energy to the ZPF whose detection is attempted. We find that the ZPF can, on the other hand, be observed from deexcitation of an active detector. We also make the connection between these statements and the recent discussion of whether decoherence can be caused by the ZPF. The distinction is made between decoherence via making a real excitation in the environment and effects due to its polarization by virtual excitations.

DOI
10.1103/physrevb.62.r10637

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We discuss the detection of quantum fluctuations in the light of the relationship between time-dependent correlators and measurable properties [L. Van Hove, Phys. Rev 95, 249 (1954)]. Considering the interaction between the fluctuating electron system and a resonant circuit or a photon mode, we prove that zero-point fluctuations (ZPF) are not observable by a passive detector, corroborating the results of Lesovik and Loosen (Pis'ma Zh. 'Eksp. Teor. Fiz. [JETP Lett. 65, 269 (1997)]). By a passive detector we mean one which is itself effectively in the ground state, and cannot transfer energy to the ZPF whose detection is attempted. We find that the ZPF can, on the other hand, be observed from deexcitation of an active detector. We also make the connection between these statements and the recent discussion of whether decoherence can be caused by the ZPF. The distinction is made between decoherence via making a real excitation in the environment and effects due to its polarization by virtual excitations.
I assume that everywhere in space there is a real random electromagnetic radiation, or zeropoint field (ZPF), which looks similar for all inertial observers, so that the stochastic properties of the field should be Lorentz invariant. This fixes the spectrum except for a single adjustable parameter measuring the scale, which is identified with Planck's constant, so making the ZPF identical to the quantum electromagnetic vacuum. Photons are just fluctuations of the random field or, equivalently, wavepackets in the form of needles of radiation superimposed to the ZPF. Two photons are "classically correlated" if the correlation involves just the intensity above the average energy of the ZPF, but they are "entangled" if the ZP fields in the neighbourhood of the photons are also correlated. These assumptions may explain all quantum optical phenomena involving radiation and macroscopic bodies, provided the latter may be treated as classical. That is, we have an interpretation of quantization for light but not for matter. Detection of photons involves subtracting the ZPF, which cannot be made without a fundamental uncertainty. This explains why photon counters cannot be manufactured with 100% efficiency and no noise (dark rate), which prevents the violation of a genuine Bell inequality (this is the so-called detection loophole). The theory thus obtained agrees very closely with standard quantum optics if this is formulated in the Wigner representation.
Detection of the quantum fluctuations by conventional methods meets certain obstacles, since it requires high-frequency measurements. Moreover, quantum fluctuations are normally dominated by classical noise and are usually further obstructed by various accompanying effects such as a detector backaction. In the present work, we demonstrate that these difficulties can be bypassed by performing the cross-correlation measurements. We propose to use a pair of two-level detectors, weakly coupled to a collective mode of an electric circuit. Fluctuations of the current source accumulated in the collective mode induce stochastic transitions in the detectors. These transitions are then read off by quantum-point contact (QPC) electrometers and translated into two telegraph processes in the QPC currents. Since both detectors interact with the same collective mode, this leads to a certain fraction of the correlated transitions. These correlated transitions are fingerprinted in the cross correlations of the telegraph processes, which can be detected at zero frequency, i.e., with long-time measurements. Concerning the dependance of the cross correlator on the detectors' energy splittings ${\ensuremath{\varepsilon}}_{1}$ and ${\ensuremath{\varepsilon}}_{2}$, the most interesting region is at the degeneracy points ${\ensuremath{\varepsilon}}_{1}=\ifmmode\pm\else\textpm\fi{}{\ensuremath{\varepsilon}}_{2}$, where it exhibits a sharp nonlocal resonance, that stems from higher-order processes. We find that at certain conditions, the main contribution to this resonance comes from the quantum noise. Namely, while the resonance line shape is weakly broadened by the classical noise, the height of the peak is directly proportional to the square of the quantum component of the noise spectral function.
Noise that can be attributed to vacuum fluctuations, usually referred to as quantum noise, is examined. It is shown that vacuum fluctuations of a single uncoupled mode do not constitute noise, in the sense of a random process, but the superposition of the fluctuations of a large number of modes does constitute, formally, noise. The effect of vacuum fluctuations of the free-space radiation field on a harmonic oscillator, a nondegenerate parametric amplifier, and a degenerate parametric amplifier, all driven by a prescribed sinusoidal field, is compared with the effect of classical noise. It is found that the coordinates of all systems respond in a formally similar manner to both vacuum fluctuations and classical noise. However, the resonance fluorescence spectrum---the evidence of ``detection''---is completely different for the two kinds of noise. The spectrum of the harmonic oscillator does not exhibit noise in response to vacuum fluctuations, but does so in response to classical noise. The spectra of the two types of parametric amplifiers do exhibit noise in response to vacuum fluctuations, but this noise differs from that in the classical case. An explanation for the difference is offered, based on the fact that the quantum fluctuations cannot do work, but can noise-modulate power from an outside source, which, for the parametric amplifiers, is the pump. In the analysis of noise from the degenerate parametric amplifier, it is shown that squeezed noise, viewed as an oscillation of the dispersion with a sufficiently low minimum, is generated in the same manner in the case of classical noise as in the case of quantum noise, and is due to phase conjugation.
The method of phenomenological damping developed by Pitaevskii (Zh. Eksp. Teor. Fiz. 35, 408 (1958) [Sov. Phys. JETP 35, 282 (1959)]) for superfluidity near the $\ensuremath{\lambda}$ point is simulated numerically for the case of a dilute, alkali, inhomogeneous Bose-condensed gas near absolute zero. We study several features of this method in describing the damping of excitations in a Bose-Einstein condensate. In addition, we show that the method may be employed to obtain numerically accurate ground states for a variety of trap potentials.