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arXiv:cond-mat/0605509 · Physical Review B

Spin current and shot noise from a quantum dot coupled to a quantized cavity field

Ivana Djuric, Christopher P. Search

Published Sep 26, 2006• 27 citations
arXivHTMLPDF

Abstract

We examine the spin current and the associated shot noise generated in a quantum dot connected to normal leads with zero bias voltage across the dot. The spin current is generated by spin flip transitions induced by a quantized electromagnetic field inside a cavity with one of the Zeeman states lying below the Fermi level of the leads and the other above. In the limit of strong Coulomb blockade, this model is analogous to the Jaynes-Cummings model in quantum optics. We also calculate the photon current and photon current shot noise resulting from photons leaking out of the cavity. We show that the photon current is equal to the spin current and that the spin current can be significantly larger than for the case of a classical driving field as a result of cavity losses. In addition to this, the frequency-dependent spin (photon) current shot noise show dips (peaks) that are a result of the discrete nature of photons.

DOI
10.1103/physrevb.74.115327

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We examine the spin current and the associated shot noise generated in a quantum dot connected to normal leads with zero bias voltage across the dot. The spin current is generated by spin flip transitions induced by a quantized electromagnetic field inside a cavity with one of the Zeeman states lying below the Fermi level of the leads and the other above. In the limit of strong Coulomb blockade, this model is analogous to the Jaynes-Cummings model in quantum optics. We also calculate the photon current and photon current shot noise resulting from photons leaking out of the cavity. We show that the photon current is equal to the spin current and that the spin current can be significantly larger than for the case of a classical driving field as a result of cavity losses. In addition to this, the frequency-dependent spin (photon) current shot noise show dips (peaks) that are a result of the discrete nature of photons.
We exploit the pumped spin-current and current noise spectra under equilibrium conditions in a single quantum dot connected to two normal leads as an electrical scheme for detection of the electron spin resonance (ESR) and decoherence. We propose spin-resolved quantum rate equations with correlation functions in Laplace space for the analytical derivation of the zero-frequency auto- and cross-shot noise spectra of charge and spin current. Our results show that in the strong Coulomb blockade regime, ESR-induced spin flip generates a finite spin current and quantum partition noises in the absence of net charge transport. Moreover, spin shot noise is closely related to the magnetic Rabi frequency and decoherence and would be a sensitive tool to measure them.
We study multiphoton blockade and photon-induced tunneling effects in the two-photon Jaynes-Cummings model, where a single-mode cavity field and a two-level atom are coupled via a two-photon interaction. We consider both the cavity-field-driving and the atom-driving cases and find that single-photon blockade and photon-induced tunneling effects can be observed when the cavity mode is driven, while the two-photon blockade effect appears when the atom is driven. For the atom-driving case (the two-photon transition process), we present a criterion of the correlation functions for the multiphoton blockade effect. Specifically, we show that quantum interference can enhance the photon blockade effect in the single-photon cavity-field-driving case. Our results are confirmed by analytically and numerically calculating the correlation function of the cavity-field mode. Our work has potential applications in quantum information processing and paves the way for the study of multiphoton quantum coherent devices.
A quantum dot interacting with two resonant cavity modes is described by a two-mode Jaynes-Cummings model. Depending on the quantum dot energy level scheme, the interaction of a singly doped quantum dot with a cavity photon generates entanglement of electron spin and cavity states or allows one to implement a SWAP gate for spin and photon states. An undoped quantum dot in the same structure generates pairs of polarization entangled photons from an initial photon product state. For realistic cavity loss rates, the fidelity of these operations is of order 80%.
The voltage probe model is a model of incoherent scattering in quantum transport. Here we use this model to study the effect of spin-flip scattering on electrical conduction through a quantum dot with chaotic dynamics. The spin decay rate $\ensuremath{\gamma}$ is quantified by the correlation of spin-up and spin-down current fluctuations (spin-flip noise). The resulting decoherence reduces the ability of the quantum dot to produce spin-entangled electron-hole pairs. For $\ensuremath{\gamma}$ greater than a critical value ${\ensuremath{\gamma}}_{c}$, the entanglement production rate vanishes identically. The statistical distribution $P({\ensuremath{\gamma}}_{c})$ of the critical decay rate in an ensemble of chaotic quantum dots is calculated using the methods of random-matrix theory. For small ${\ensuremath{\gamma}}_{c}$ this distribution is $\ensuremath{\propto}{\ensuremath{\gamma}}_{c}^{\ensuremath{-}1+\ensuremath{\beta}∕2}$, depending on the presence $(\ensuremath{\beta}=1)$ or absence $(\ensuremath{\beta}=2)$ of time-reversal symmetry. To make contact with experimental observables, we derive a one-to-one relationship between the entanglement production rate and the spin-resolved shot noise, under the assumption that the density matrix is isotropic in the spin degrees of freedom. Unlike the Bell inequality, this relationship holds for both pure and mixed states. In the tunneling regime, the electron-hole pairs are entangled if and only if the correlator of parallel spin currents is at least twice larger than the correlator of antiparallel spin currents.
The basic equations governing noise phenomena are derived from first principles and applied to examples in optical communications. Quantum noise arises from two sources, the momentum fluctuations of electrons at optical frequencies and the uncertainty-related fluctuations of the electromagnetic field. Shot noise results from the beating of the noise sources with the signal field. In high-gain amplifiers, the spontaneous-emission noise dominates shot noise and results in a noise figure of at least 3 dB. It is shown explicitly how, at high power, both the laser field and the laser noise source become classical. The increase in noise in lasers with open cavities is not due to enhanced spontaneous emission as once thought, but to single-pass amplification. The noise fields and spontaneous currents have Gaussian distributions, while nonlasing modes have exponential photon-number distributions. Low-frequency intensity fluctuations arise from the electric current driving the laser and can be sub-Poissonian, in contrast to shot noise, which has a Poissonian distribution. The calculational tools are a wave equation for the field operator and a rate equation for the carrier-number operator, each containing spontaneous current noise sources. The correlation functions of these sources are determined by the fluctuation-dissipation theorem. [S0034-6861(96)00503-X]
The quantum dynamics of a double quantum dot two-level system, coupled to a leaking microwave resonator mode, is theoretically investigated. The double quantum dot is driven by applying a continuous field giving rise to time-dependent modulations of its energy separation between the ground levels of each dot, forming the qubit. Therefore, the cavity resonances occur when the difference between the resonator and the qubit frequencies equals the multiple of the modulation frequency, respectively. In the strong Coulomb interaction limit and the weak couplings of the combined system, i.e. the qubit and the single-mode cavity, to corresponding electronic, phononic or photonic reservoirs, we have demonstrated that the output cavity electromagnetic field is formed of a single-photon flux obeying the sub-Poissonian quantum photon statistics. This was proved via Fano's factor behaviour or by comparing the resonator's second- and third-order photon correlation functions, respectively. The phonon, the cavity mode dephasing or the environmental temperatures influence on the quantum properties of the photons are also discussed.