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Dissipation-induced squeezing in mesoscopic branching circuits

R.C. Liu, Y. Yamamoto

Published May 8, 1994• 0 citations
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Abstract

A partitioned system of electrons is mathematically equivalent to an assembly of two- level atoms described by spin operators. The spin-operator uncertainty relation can therefore be interpreted as a number-phase- uncertainty relation for the partition of a single electron. This electron-number uncertainty manifests as a current-difference noise in the output leads of the mesoscopic branching circuit. Similarly, the phase uncertainty is revealed by the properly normalized current-difference fluctuations of the output leads for an interferometric geometry.

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A partitioned system of electrons is mathematically equivalent to an assembly of two- level atoms described by spin operators. The spin-operator uncertainty relation can therefore be interpreted as a number-phase- uncertainty relation for the partition of a single electron. This electron-number uncertainty manifests as a current-difference noise in the output leads of the mesoscopic branching circuit. Similarly, the phase uncertainty is revealed by the properly normalized current-difference fluctuations of the output leads for an interferometric geometry.
A partitioned system of fermions is mathematically equivalent to an assembly of two-level atoms described by spin operators. A number-phase uncertainty relation can therefore be derived to describe the noise properties of divided electrons. We examine both the number (or electron flux) and phase (or electron wave phase) decorrelation introduced by electron branching in mesoscopic circuits. Initially Poissonian, this electron number partition noise is increasingly suppressed by inelastic scattering in the transition from ballistic to dissipative electron division. Graphical results from our model show a trend from a coherent spin state in the ballistic regime toward a number-squeezed spin state in the dissipative regime, even when detrimental elastic scattering is present.
Using the path integral method we derive quantum wave function and quantum fluctuations of charge and current in the mesoscopic RLC circuit. We find that the quantum fluctuation of charge decreases with time, oppositely, the quantum fluctuation of current increases with time monotonously. Therefore there is a squeezing effect in the circuit. If some more charge devices are used in the mesoscopic-damped circuit, the quantum noise can be reduced. We also find that uncertainty relation of charge and current periodically varies with the period π/2 in the under-damped case.
The quantum fluctuations of the charge and current in a non-dissipative mesoscopic circuit with coupled inductors and capacitors are studied for the squeezed vacuum state. The influence of the phase angle upon the quantum fluctuations is discussed in particular. Our results indicate that when the circuit parameters remain constant and the phases θ of the two circuits are equal, the squeezing of the charge or its conjugate variable increases. When the difference of the two phases equals π, the squeezing will deteriorate. Therefore, if we want to decrease the quantum noise, we should not only control the amplitude r , but also control the phase θ carefully.
Amplitude fluctuations in the light from a laser and the partition noise attributable to a beam splitter are analyzed using an equivalent-circuit model that incorporates amplitude squeezing. When the energy is not carried by photons but by electrons and also when electrons can be treated as classical particles, the circuit model need not be changed. One simply applies the general circuit model to low frequencies h\ensuremath{\nu}\ensuremath{\ll}kB{\mathit{k}}_{\mathit{B}}kB​T. Conversion of an electric current to photon flux, and vice versa, converts classical sub-shot-noise spectra of electric currents into quantum squeezing of photon fluxes, and vice versa. The sub-shot-noise character of electric currents, unlike that of quantum squeezing, is not necessarily destroyed by current loss.