  We investigate the temperature-driven quantum-to-classical crossover in a
single-electron emitter. The emitter is composed of a quantum conductor and an
electrode, which is coupled via an Ohmic contact. At zero temperature, it has
been shown that a single electron can be injected coherently by applying an
unit-charge Lorentzian pulse on the electrode. As the electrode temperature
increases, we show that the electron emission approaches a time-dependence
Poisson process at long times. The Poissonian character is demonstrated from
the time-resolved full counting statistics. In the meantime, we show that the
emission events remain correlated, which is due to the Pauli exclusion
principle. The correlation is revealed from the emission rates of individual
electrons, from which a characteristic correlation time can be extracted. The
correlation time drops rapidly as the electrode temperature increases,
indicating that correlation can only play a non-negligible role at short times
in the high-temperature limit. By using the same procedure, we further show
that the quantum-to-classical crossover exhibits similar features when the
emission is driven by a Lorentzian pulse carrying two electron charge. Our
results show how the electron emission process is affected by thermal
fluctuations in a single-electron emitter.
