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Physics
Condensed Matter Physics

High-temperature fusion of a multi-electron leviton

Profile image of Mykhailo MoskaletsMykhailo Moskalets

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 multi-electron injection, the situation is more subtle. 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, what 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 N e at high temperatures. It looks like the exchange correlations glue up 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 → ∞, the correlation contribution completely suppresses the effect of temperature on noise.

Figures (7)
FIG. 1: A multi-particle electronic state |N) emitted by the source S and incoming to the wave splitter (a grey rectangle) gives rise the two outgoing currents, J3 and J4. The correla- tion function of these currents is used to gain information on the incoming quantum state.
FIG. 1: A multi-particle electronic state |N) emitted by the source S and incoming to the wave splitter (a grey rectangle) gives rise the two outgoing currents, J3 and J4. The correla- tion function of these currents is used to gain information on the incoming quantum state.
Importantly, the component wave functions at different energies, « # ¢’, are not orthogonal any longer. As a result, the correlation noise arises, PS9"" # 0. Substituting Eq. (9) into Eq. (3) we find the individual and correlation noise to be the following, The correlation function above tells us that the source now emits particles that are not in a pure state. The jth electron is now in a mixed quantum state with probabil- ity density pe («) = —Of/Oe and with component wave functions WV, .. To be specific, on further on I focus on the source of levitons.
Importantly, the component wave functions at different energies, « # ¢’, are not orthogonal any longer. As a result, the correlation noise arises, PS9"" # 0. Substituting Eq. (9) into Eq. (3) we find the individual and correlation noise to be the following, The correlation function above tells us that the source now emits particles that are not in a pure state. The jth electron is now in a mixed quantum state with probabil- ity density pe («) = —Of/Oe and with component wave functions WV, .. To be specific, on further on I focus on the source of levitons.
FIG. 2: The temperature dependence of a single-particle shot noise, P34 = —P3a, Eq. (14). The parameter kp0* = Ez/r.
FIG. 2: The temperature dependence of a single-particle shot noise, P34 = —P3a, Eq. (14). The parameter kp0* = Ez/r.
where €, = fh/(20,) is the energy of a 1-particle leviton®®. The individual contribution is the same for all particles at nonzero temperatures, as it was at zero temperature,
where €, = fh/(20,) is the energy of a 1-particle leviton®®. The individual contribution is the same for all particles at nonzero temperatures, as it was at zero temperature,
FIG. 3: The temperature dependence of the shot noise of a 5-particle leviton. The individual contribution is given in Eq. (14) with N = 5. The correlation contribution is defined in Eqs. (11), (12), and (13) with N = 5. The dashed red line represents the high-temperature asymptotics of the total noise, see Eq. (15) with N = 5. The parameter kp0* = E,/7.
FIG. 3: The temperature dependence of the shot noise of a 5-particle leviton. The individual contribution is given in Eq. (14) with N = 5. The correlation contribution is defined in Eqs. (11), (12), and (13) with N = 5. The dashed red line represents the high-temperature asymptotics of the total noise, see Eq. (15) with N = 5. The parameter kp0* = E,/7.
FIG. 4: The temperature dependence of the shot noise per particle in the macroscopic limit, N — oo. The individual contribution is given in Eq. (14): limy— oo Pyn4 /N = —PA,. The correlation contribution is given in Eq. (16). The param- eter kpO* = Ez /n.
FIG. 4: The temperature dependence of the shot noise per particle in the macroscopic limit, N — oo. The individual contribution is given in Eq. (14): limy— oo Pyn4 /N = —PA,. The correlation contribution is given in Eq. (16). The param- eter kpO* = Ez /n.
The individual contribution is the same for all particles, so it is additive, that is, it is proportional to the num- ber of particles N. The correlation contribution of each pair of particles is the same, so it is proportional to the number of pairs, N(N — 1).
The individual contribution is the same for all particles, so it is additive, that is, it is proportional to the num- ber of particles N. The correlation contribution of each pair of particles is the same, so it is proportional to the number of pairs, N(N — 1).

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