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arXiv:1709.03334 · Physical review. B./Physical review. B

Single-particle shot noise at nonzero temperature

Michael V. Moskalets

Published Oct 13, 2017• 15 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.96.165423

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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 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, $N\ensuremath{\rightarrow}\ensuremath{\infty}$, the correlation contribution completely suppresses the effect of temperature on 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.
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.
A point contact in a Luttinger liquid couples left- and right-moving channels, producing shot noise. We calculate exactly the dc shot noise at zero temperature in the out-of-equilibrium steady state where current is flowing. Integrability ensures the existence of a quasiparticle basis where scattering is ``one by one'' off the point contact, enabling us to generalize the Landauer approach to shot noise to this interacting model. Experiments in a fractional quantum Hall effect device should test our results, providing a clear signal of the fractional charge of the Laughlin quasiparticles.
We develop an open quantum theory for shot-noise dynamics in dissipative chiral transport. By mapping a system under consideration onto a quantum circuit, we show that current noise is governed by two competing factors: the average occupancy distribution and particle-number fluctuations. With energy fully relaxed, shot noise is strongly suppressed, reflecting the stacking of electrons into lower energy states due to dissipation. This process quenches the partition noise from partially occupied levels, and finally isolates the residual noise protected by strong U(1)U(1)U(1) symmetry. Moreover, selectively heating the source against the bath uncovers the underlying competition between the noise contributions from the occupancy distribution and those from the particle-number fluctuations. It triggers a sign reversal in inter-channel correlation noise, a signature masked by seemingly identical single-channel thermal noises. We propose an inversion scheme to experimentally reconstruct the hidden occupancy distribution directly from measurable noise cumulants.