Single-particle shot noise at nonzero temperature

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.

Figure 1

A mesoscopic electron collider circuit with two input and two output chiral electron waveguides (shown as blue straight lines) coupled via an electron wave splitter (shown as a rounded rectangle). Two incoming states $|{\mathrm{\Psi }}_{\alpha }^{\mathrm{in}}\rangle ,\alpha =1,2$, are scattered on the wave splitter. As a result the two outgoing currents $I_{\beta }^{\mathrm{out}},\beta =3,4$ are generated.

Figure 2

The shot noise, ${\mathcal{P}}_{34}^p$, Eq. (8a), (a blue solid line) caused by partitioning a leviton per period $\mathcal{T}$ on a wave splitter with transmission probability $T$, is shown as a function of the temperature $\theta$, at which a leviton is created. The constant ${\mathcal{P}}_0=e^{2}T\left(1-T\right)/\mathcal{T}$ is a (minus) zero-temperature shot noise. The characteristic temperature $k_B{\theta }^{★}={\mathcal{E}}_L/\pi$ is defined by the energy ${\mathcal{E}}_L=\hslash /\left(2{\mathrm{\Gamma }}_{\tau }\right)$ of a leviton of duration $2{\mathrm{\Gamma }}_{\tau }$. The high temperature asymptotics, Eq. (8c), is shown as a red dashed line.

Figure 3

The correlation correction to the shot noise of levitons, ${\mathcal{P}}_{34}^{\mathrm{corr}}$, Eq. (9), (a blue solid line) is shown as a function of temperature $\theta$. The high temperature asymptotics, Eq. (9c), is shown as a red dashed line. The units are the same as in Fig. 2.

Figure 4

The antibunching correction to the shot noise of a leviton created at zero temperature, ${\mathcal{P}}_{34}^{\mathrm{ab}}$, Eq. (10b), is shown as a function of temperature of thermal excitations, ${\theta }_2=\theta$. The units are the same as in Fig. 2.