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arXiv:1801.04787 · Physical review. B./Physical review. B

High-temperature fusion of a multielectron leviton

Michael V. Moskalets

Published Apr 11, 2018• 13 citations
arXivHTMLPDF

Abstract

The state of electrons injected onto the surface of the Fermi sea depends on temperature. The state is pure at zero temperature and is mixed at finite temperature. In the case of a single-electron injection, such a transformation can be detected as a decrease in shot noise with increasing temperature. In the case of a multielectron injection, the situation is subtler. The mixedness helps the development of quantum-mechanical exchange correlations between injected electrons, even if such correlations are absent at zero temperature. These correlations enhance the shot noise, which in part counteracts the reduction of noise with temperature. Moreover, at sufficiently high temperatures, the correlation contribution to noise predominates over the contribution of individual particles. As a result, in the system of $N$ electrons, the apparent charge (which is revealed via the shot noise) is changed from $e$ at zero temperature to $Ne$ at high temperatures. It looks like the exchange correlations glue electrons into one particle of total charge and energy. This point of view is supported by both charge noise and heat noise. Interestingly, in the macroscopic limit, $N\ensuremath{\rightarrow}\ensuremath{\infty}$, the correlation contribution completely suppresses the effect of temperature on noise.

DOI
10.1103/physrevb.97.155411

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The state of electrons injected onto the surface of the Fermi sea depends on temperature. The state is pure at zero temperature and is mixed at finite temperature. In the case of a single-electron injection, such a transformation can be detected as a decrease in shot noise with increasing temperature. In the case of a multielectron injection, the situation is subtler. The mixedness helps the development of quantum-mechanical exchange correlations between injected electrons, even if such correlations are absent at zero temperature. These correlations enhance the shot noise, which in part counteracts the reduction of noise with temperature. Moreover, at sufficiently high temperatures, the correlation contribution to noise predominates over the contribution of individual particles. As a result, in the system of NNN electrons, the apparent charge (which is revealed via the shot noise) is changed from eee at zero temperature to NeNeNe at high temperatures. It looks like the exchange correlations glue electrons into one particle of total charge and energy. This point of view is supported by both charge noise and heat noise. Interestingly, in the macroscopic limit, N\ensuremath→\ensuremath∞N\ensuremath{\rightarrow}\ensuremath{\infty}N\ensuremath→\ensuremath∞, the correlation contribution completely suppresses the effect of temperature on noise.
The state of a single particle injected onto the surface of the Fermi sea is a pure state if the temperature is zero and is a mixed state if the temperature is finite. Moreover, the state of an injected particle is orthogonal to the state of the Fermi sea at zero temperature, while it is not orthogonal at nonzero temperature. These changes in the quantum state of the injected particles can be detected using the temperature dependence of the shot noise that is generated when the particles one by one pass through a semitransparent quantum point contact. Namely, the shot noise produced by the mixed state is suppressed in comparison with the noise of the pure state. In addition, the correlations between the injected particles and the underlying Fermi sea, present at nonzero temperature, do enhance the shot noise. Furthermore, antibunching of injected particles with possible thermal excitations coming from another input channel of a quantum point contact does suppress shot noise. Here I analyze in detail these three effects, which are responsible for the temperature dependence of the shot noise, and discuss how to distinguish them experimentally.
The state of particles injected onto the surface of the Fermi sea depends essentially on the temperature. The pure state injected at zero temperature becomes a mixed state if injected at finite temperature. Moreover the electron source injecting a single-particle state at zero temperature may excite a multi-particle state if the Fermi sea is at finite temperature. Here I unveil a symmetry of the scattering amplitude of a source, which is sufficient to preserve a single-particle emission regime at finite temperatures if such a regime is achieved at zero temperature. I give an example and analyze the effect of temperature on time-dependent electrical and heat currents carried by a single-particle excitation.
The single-particle state is not expected to demonstrate second-order coherence. Here I analyze the injection of electrons into a conductor and show that, at a nonzero temperature, the underlying Fermi sea causes the single-particle injected state to exhibit second-order coherence. For this purpose, I calculate the second-order correlation function, G(2){G}^{(2)}G(2), of electrons injected on top of the Fermi sea. At zero temperature, the function G(2){G}^{(2)}G(2) unambiguously demonstrates whether the injected state is a single- or a multiparticle state: G(2){G}_{}^{(2)}G(2)​ vanishes in the former case, while it does not vanish in the latter case. However, at nonzero temperatures, when the injected state is a mixed state, a purely single-particle contribution makes the function G(2){G}_{}^{(2)}G(2)​ nonvanishing even in the case of injection of one electron. The single-particle contribution puts the lower limit on the second-order correlation function and thereby limits its use as a single-particle injection test at nonzero temperatures. The existence of a single-particle contribution to G(2){G}_{}^{(2)}G(2)​ can be verified experimentally by measuring the cross-correlation electrical noise.
The state of particles injected onto the surface of the Fermi sea depends essentially on the temperature. The pure state injected at zero temperature becomes a mixed state if injected at finite temperature. Moreover the electron source injecting a single-particle state at zero temperature may excite a multi-particle state if the Fermi sea is at finite temperature. Here I unveil a symmetry of the scattering amplitude of a source, which is sufficient to preserve a single-particle emission regime at finite temperatures if such a regime is achieved at zero temperature. I give an example and analyze the effect of temperature on time-dependent electrical and heat currents carried by a single-particle excitation.
We study in detail a system of two interferometers aimed at detecting extremely faint phase fluctuations. This system can represent a breakthrough for detecting a faint correlated signal that would remain otherwise undetectable even using the most sensitive individual interferometric devices, as in the case of so-called holographic noise. The signature of this kind of noise emerges as a correlation between the output signals of the interferometers. On the other hand, when holographic noise is absent one expects uncorrelated signals since the time-averaged fluctuations due to shot noise and other independent contributions vanish (though limiting the overall sensitivity). We show how injecting quantum light in the free ports of the interferometers can reduce the photon noise of the system beyond the shot noise, enhancing the resolution in the phase-correlation estimation. We analyze the use of both the two-mode squeezed vacuum and two independent squeezed states. Our results confirm the benefit of using squeezed beams together with strong coherent beams in interferometry. We also investigate the possible use of the two-mode squeezed vacuum, discovering interesting and unexplored areas of application of bipartite entanglement, in particular the possibility of reaching in principle a surprising uncertainty reduction.
It is common wisdom that a better understanding of how to quantify electron correlation should lead to more efficient treatments of the correlation problem. Here, we not only substantiate this view but turn it into a concrete, systematic framework for ground states. Since prominent correlation measures such as the nonfreeness depend only on the one-particle reduced density matrix, modeling the correlation energy as a function of such a measure naturally places the framework within reduced density matrix functional theory, while keeping the cost at mean-field level. Strikingly, the variable conjugate to the measure emerges as a ``correlation temperature'', thereby connecting correlation measures, functional theory, and effective temperatures. The framework rationalizes methods such as i-DMFT, and we illustrate its key concepts analytically for the Hubbard dimer and numerically for small molecular systems. This brings a fundamental question within reach: how much of the correlation problem can be solved at mean-field cost?