Quantum stochastic resonance in a single-photon emitter

TL;DR

This work addresses how quantum noise can enhance a weak, periodically driven signal in a solid-state two-state system. The authors realize a driven single quantum dot coupled to an electron reservoir, monitor its charge state optically via resonance fluorescence, and analyze the resulting telegraph signals with full counting statistics, including the Fano factor $F$ and normalized factorial cumulants $x_m$. They observe a quantum stochastic resonance manifested as a dip in $F$ and peaks in $x_m$, with the resonance frequency $f_{ m res}$ depending on drive amplitude and shifting with cumulant order; analytic limits provide simple relations for $T_{ m res}$ in linear and strong-drive regimes. The work demonstrates quantum stochastic resonance in a controllable emitter and introduces normalized factorial cumulants as a powerful tool for probing discrete quantum transport, with potential implications for regulating photon streams in quantum networks.

Abstract

Stochastic resonance is a phenomenon in which fluctuations enhance an otherwise weak signal. It has been found in many different systems in paleoclimatology, biology, medicine, and physics. The classical stochastic resonance due to thermal noise has recently been experimentally extended to the quantum regime, where the fundamental randomness of individual quantum events provides the noise source. Here, we demonstrate quantum stochastic resonance in the single-electron tunneling dynamics of a periodically driven single-photon emitter, consisting of a self-assembled quantum dot that is tunnel-coupled to an electron reservoir. Such highly-controllable quantum emitters are promising candidates for future applications in quantum information technologies. We monitor the charge dynamics by resonant optical excitation and identify quantum stochastic resonance with the help of full counting statistics of tunneling events in terms of the Fano factor and extend the statistical evaluation to factorial cumulants to gain a deeper understanding of this far-reaching phenomenon.

Figures (6)

• Figure 1: Resonance fluorescence in a single quantum dot.a The excitation laser is reflected onto the sample by a 90:10 beamsplitter. Two crossed polarisers are used to suppress the reflected laser light. The QDs are embedded in a p-i-n-diode structure between a gate electrode at the top and an electron reservoir at the bottom of the structure. A gate voltage $V_g$ can be applied to control the QD charge state and its transition energies. b Exciton transition $X^0$ as a function of the laser excitation frequency and applied gate voltage. At a gate voltage of $V_g=0.5\,$V, the QD is charged with an electron from the reservoir and the $X^0$ transition can no longer be excited by the resonant laser. The insets show schematically the two situations around the transition voltage at $V_g=0.5\,$V, where the chemical potential $\mu$ is below (left inset) and above (right inset) of the lowest quantum dot state.
• Figure 2: The electron dynamics, revealed in the optical resonance fluorescence signal.a Electron tunneling rates $\gamma_{In}$ and $\gamma_{Out}$ as a function of the gate voltage $V_g$. Solid lines are fits to the data, given by the Fermi-distribution in the electron reservoir. The insets illustrate the continuous increase of $\gamma_{In}$ with increasing gate voltage, while $\gamma_{Out}$ decreases with increasing chemical potential with respect to the QD level. Around the gate voltage where both rates are equal, the voltage modulation for the quantum stochastic resonance takes place. The error bars are derived via $R^2$ of the exponential fit presented in Ref. Zollner.2024. b Telegraph signals with a binning of $100\,\mu$s, showing the single electron tunneling events between the quantum dot and the reservoir as a switching on and off of the resonance fluorescence signal. For no modulation the electron tunnels in and out randomly with fixed rates $\gamma_{In}$ and $\gamma_{Out}$. When the modulation of the gate voltage is on, correlations start to occur between the electron tunneling and $V_g$. This is shown with shaded areas as a guide to the eye where a switching event should occur for deterministic transport. The amplitude of the a. c. drive is indicated as a scale bar in a.
• Figure 3: Probability distribution of electron transport. Probability distribution $P_N(\Delta t=5\,$ms) (red dots) for the number of electrons transferred at a modulation frequency of $f_{mod}=796\,$Hz with amplitude $16\,$mV. The experimental data is compared to a Kronecker distribution (gray), corresponding to completely regular switching, and a Poisson distribution (blue line) as an completely uncorrelated transport. The measured distribution is narrower than a Poisson distribution for the same mean value. The reduced width of a distribution indicates a more regular electron transport.
• Figure 4: Time evolution of the Fano factor.a The Fano factor versus the time interval $\Delta t$ for selected modulation frequencies from $52\,$Hz (light blue) to $5\,$kHz (dark blue) and a modulation amplitude of $16\,$mV. At a driving frequency of 796Hz, the Fano factor is at a minimum for all $\Delta t$, indicating stochastic resonance around this frequency. The dashed line is at the time intervall of $\Delta t=20\,$ms, where we define the long time limit (see subsection Fano factor). The maxima of the Fano factor marked with black dots are artefacts that occur when the time interval $\Delta t$ is half of the modulation period $T_{mod}$; schematically shown in the inset and explained in more detail in the main text. b The long time limit of the Fano factor for different binning times $t_{bin}$ of the single photon stream. The decrease in the Fano factor at $\approx800\,$Hz is due to the quantum stochastic resonance.
• Figure 5: Quantum stochastic resonance indicated by the Fano factor.a Fano factor as a function of the modulation frequency for different modulation amplitudes (data points) compared with theoretical model curves (solid blue lines). The model has no fitting parameters. The modulation is symmetrical around $V_g=496\,$mV, where $\gamma_{In}=\gamma_{Out}$. The minimum around $\approx800\,$Hz is due to quantum stochastic resonance. The dashed vertical line is given by Eq. \ref{['eq:f_res_linear']} for a $1\,$mV modulation. b The Fano factor as a function of the modulation frequency for $16\,$mV and $87\,$mV. The exact values of the upper, lower and average value of the gate voltage are given in Table S1 in supplementary note 3. The vertical lines are given by Eq. \ref{['eq:f_res_nonlinear']} for a $16\,$mV and $87\,$mV modulation.