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arXiv:1803.02175 · Physical review. B./Physical review. B

Coherent dynamics in stochastic systems revealed by full counting statistics

Philipp Stegmann, Jürgen König, S. Weiss

Published Jul 6, 2018• 20 citations
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Abstract

Stochastic systems feature, in general, both coherent dynamics and incoherent transitions between different states. We propose a method to identify the coherent part in the full counting statistics for the transitions. The proposal is illustrated for electron transfer through a quantum-dot spin valve, which combines quantum-coherent spin precession with electron tunneling. We show that by counting the number of transferred electrons as a function of time, it is possible to distill out the coherent dynamics from the counting statistics even in transport regimes, in which other tools such as the frequency-dependent current noise and the waiting-time distribution fail.

DOI
10.1103/physrevb.98.035409

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A theory of electron counting statistics in quantum transport is presented. It involves an idealized scheme of current measurement using a spin 1/2 coupled to the current so that it precesses at the rate proportional to the current. Within such an approach, counting charge without breaking the circuit is possible. As an application, we derive the counting statistics in a single channel conductor at finite temperature and bias. For a perfectly transmitting channel the counting distribution is gaussian, both for zero-point fluctuations and at finite temperature. At constant bias and low temperature the distribution is binomial, i.e., it arises from Bernoulli statistics. Another application considered is the noise due to short current pulses that involve few electrons. We find the time-dependence of the driving potential that produces coherent noise-minimizing current pulses, and display analogies of such current stateswith quantum-mechanical coherent states.
We investigate the dynamics of electron spin qubits in quantum dots. Measurement of the qubit state is realized by a charge current through the dot. The dynamics is described in the framework of the quantum trajectory approach, widely used in quantum optics. The relevant master equation dynamics is unraveled to simulate stochastic tunneling events of the current through the dot. Quantum trajectories are then used to extract the counting statistics of the current. We show how, in combination with an electron spin resonance field, counting statistics can be employed for quantum-state tomography of the qubit state. Further, it is shown how decoherence and relaxation time scales can be estimated with the help of counting statistics, in the time domain.
We demonstrate that the probability distribution of the net number of electrons passing through a quantum system in a junction obeys a steady-state fluctuation theorem (FT) which can be tested experimentally by the full counting statistics (FCS) of electrons crossing the lead-system interface. The FCS is calculated using a many-body quantum master equation combined with a Liouville space generating function formalism. For a model of two coupled quantum dots, we show that the FT becomes valid for long binning times, and provide an estimate for the finite-time deviations. The Mandel (or Fano) parameter associated with the incoming or outgoing electron transfers shows sub-Poissonian (antibunching) statistics.
Quantum entanglement between electrons in nanostructures is a key concept of quantum information still waiting to be experimentally demonstrated. In this master's thesis we present and analyze the full counting statistics of the charge transfer of a sextuple quantum dot system which works as both entangler and detector of spatially separated electrons. Under certain resonance conditions the system operates in the co-tunneling regime, limiting environment-induced decoherence. By means of a generalized Schrieffer-Wolff transformation the co-tunneling dynamics are obtained from an effective Hamiltonian. Based on these results, a master equation is derived for the reduced density operator of the open sextuple dot system and used to compute the full counting statistics. We find that the system displays quantum coherent non-local transport properties and violates Bell's inequality. Consequently, the sextuple dot system could potentially be used to experimentally demonstrate entanglement between electrons as intended.
We consider current shot noise and the full counting statistics in a chain of quantum dots which exhibits a continuous nonequilibrium phase transition as a function of the tunnel couplings of the chain with the electrodes. Using a combination of analytical and numerical methods, we establish that the full counting statistics is conventional away from the phase transition, but becomes, in a well-defined sense, essentially non-Gaussian on the critical line, where the current fluctuations are controlled by the dynamic critical exponent zzz. We find that signatures of the critical full counting statistics persist in quantum-dot chains of finite length.