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arXiv:0810.5095 · Physical Review A

Intrinsic quantum noise in Faraday-rotation measurements of a single-electron spin

Yanjun Ma, Jeremy Levy

Published Feb 24, 2009• 2 citations
arXivHTMLPDF

Abstract

Faraday rotation is one way to realize quantum nondemolition measurement of electron spin in quantum dots. To describe Faraday rotation, semiclassical models are typically used based on quantized electron-spin states and classical electromagnetic fields. Such treatments neglect the entanglement between electronic and photonic degrees of freedom that produce intrinsic quantum noise, limiting the ultimate sensitivity of this technique. We present a fully quantum-mechanical description of Faraday rotation and quantify this intrinsic noise. A method for measuring the purity of a given spin state is suggested based on this analysis.

DOI
10.1103/physreva.79.023830

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Faraday rotation is one way to realize quantum nondemolition measurement of electron spin in quantum dots. To describe Faraday rotation, semiclassical models are typically used based on quantized electron-spin states and classical electromagnetic fields. Such treatments neglect the entanglement between electronic and photonic degrees of freedom that produce intrinsic quantum noise, limiting the ultimate sensitivity of this technique. We present a fully quantum-mechanical description of Faraday rotation and quantify this intrinsic noise. A method for measuring the purity of a given spin state is suggested based on this analysis.
We propose a quantum nondemolition method---a giant optical Faraday rotation near the resonant regime to measure a single-electron spin in a quantum dot inside a microcavity where a negatively charged exciton strongly couples to the cavity mode. Left-circularly and right-circularly polarized lights reflected from the cavity obtain different phase shifts due to cavity quantum electrodynamics and the optical spin selection rule. This yields giant and tunable Faraday rotation that can be easily detected experimentally. Based on this spin-detection technique, a deterministic photon-spin entangling gate and a scalable scheme to create remote spin entanglement via a single photon are proposed.
We propose a method for quantum nondemolition (QND) measurement of one component of spin by the measurement of polarization rotation of the off-resonant light induced by a paramagnetic Faraday rotation effect. We show that nonclassical states of spins such as the squeezed spin state, the Dicke state, and macroscopic quantum superposed state of spin can be realized corresponding to particular results of QND measurements. Furthermore, it is shown that a nonclassical state of light such as the twin photon state can also be realized with this method.
The radio-frequency (rf) single-electron box is becoming an attractive charge sensor for semiconductor-based quantum computing devices due to its high sensitivity and small footprint, which facilitate the design of highly connected qubit architectures. However, an understanding of its ultimate sensitivity is missing due to the lack of a noise model. Here, we quantify the intrinsic noise of the single-electron box arising from stochastic cyclic electron tunneling between a quantum dot and a reservoir driven by a periodic gate voltage. We use both a master-equation formalism and Markov Monte Carlo simulations to calculate the gate-noise current and find that the noise mechanism can be represented as a cyclostationary process. We consider the implications of this cyclostationary noise on the ultimate sensitivity of single-electron box sensors for fast high-fidelity readout of spin qubits, in particular evaluating results for rf reflectometry implementations and the back action of the sensor on a qubit. Furthermore, we determine the conditions under which the intrinsic noise limit could be measured experimentally and techniques by which the noise can be suppressed to enhance qubit-readout fidelity. Published by the American Physical Society 2024
The field of quantum metrology concerns the physical measurement of sensors with a precision comparable to fundamental limits set by quantum mechanics. It is possible to outperform naive interpretations of these limits by using entangled states of the sensor system. One example is that of a spin-squeezed state, in which the uncertainty of one variable is decreased at the expense of another while still obeying Heisenberg's uncertainty principle, improving rotation sensitivity along a chosen axis. These states are potentially useful in devices including atomic clocks, inertial sensors, and magnetometers. Any model of a quantum metrology device must respect the fact that physical measurements are not passive, as imagined classically, but necessarily invasive. Far from being a negative feature, well-understood quantum measurement can conditionally drive a system into desirable entangled states, including spin-squeezed states. Furthermore, the fundamental randomness of this process can, in principle, be removed with real-time feedback control, motivating an adaptation of classical feedback concepts to the quantum realm. In this thesis, I describe these ideas in the context of one experimental example. A laser-cooled cloud of cesium spins is polarized along one axis via optical pumping and, subsequently, a linearly polarized far-off resonant probe beam traverses the sample. Due to the interaction Hamiltonian, the optical polarization rotates by an amount nominally proportional to one spin component of the collective spin state, enacting a weak, continuous, nondemolition measurement of that collective variable. This optical Faraday rotation is then measured with a polarimeter and the inherently noisy result used to condition the collective atomic state via a quantum filter, or stochastic master equation. Ideally, this process is capable of producing spin-squeezed states via the measurement itself. The details of this measurement are investigated in depth, including a derivation of the nonideal polarizability Hamiltonian, an analysis of the projection process with control, and a derivation of the magnetometry sensitivity. Experimentally, we demonstrate continuous measurement of the collective spin state with a large single-shot signal-to-noise ratio and verify many predictions of the model. Finally, we describe attempts to observe the atomic projection noise, which would infer the preparation of spin-squeezed states.
Paramagnetic Faraday rotation is a quantum nondemolition measurement method that can generate spin squeezing and improve the measurement precision of a collective spin component beyond the standard quantum limit. In practice, a constant bias magnetic field is used to drive the spin precessing at sufficiently high frequency in order to lift the signal out of low-frequency technical noises. However, continuous measurement of precessing spins introduces back-action noise (BAN) due to the light-shift effect. Two types of back-action-evading (BAE) measurement of collective spin components have been demonstrated recently: continuous measurement of a two-ensemble system and stroboscopic measurement of a single ensemble. Here we propose another single ensemble BAE measurement by periodically modulating the bias field with $\ensuremath{\pi}$ pulses. Our theoretical calculation shows that under experimental settings where pulse-field modulation does not introduce significant decoherences, the proposed method can suppress the BAN and generate spin squeezing faster than the stroboscopic one at the same probe light power. Moreover, if it is combined with synchronous stroboscopic probing, light-shift BAN can be completely eliminated.