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arXiv:0807.4779 · New Journal of Physics

Dynamics revealed by correlations of time-distributed weak measurements of a single spin

R-B Liu, S-H Fung, H-K Fung, Alexander N. Korotkov, Lu Jeu Sham

Published Jan 19, 2010• 23 citations
arXivHTMLPDF

Abstract

We show that the correlations in stochastic outputs of time-distributed weak measurements can be used to study the dynamics of an individual quantum object, with a proof-of-principle setup based on small Faraday rotation caused by a single spin in a quantum dot. In particular, the third-order correlation can reveal the 'true' spin decoherence, which would otherwise be concealed by the inhomogeneous broadening effect in the second-order correlations. The viability of such approaches lies in the fact that (i) in weak measurement the state collapse that would disturb the system dynamics occurs at a very low probability and (ii) a shot of measurement projecting the quantum object to a known basis state serves as a starter or stopper of the evolution without pumping or coherently controlling the system as otherwise required in conventional spin echo.

DOI
10.1088/1367-2630/12/1/013018

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We show that the correlations in stochastic outputs of time-distributed weak measurements can be used to study the dynamics of an individual quantum object, with a proof-of-principle setup based on small Faraday rotation caused by a single spin in a quantum dot. In particular, the third-order correlation can reveal the 'true' spin decoherence, which would otherwise be concealed by the inhomogeneous broadening effect in the second-order correlations. The viability of such approaches lies in the fact that (i) in weak measurement the state collapse that would disturb the system dynamics occurs at a very low probability and (ii) a shot of measurement projecting the quantum object to a known basis state serves as a starter or stopper of the evolution without pumping or coherently controlling the system as otherwise required in conventional spin echo.
We demonstrate an entirely new method to probe quantum measurement phenomena in semiconductor quantum dot (QD) spin qubits [1]. In addition to providing direct evidence for the quantum nature of solid state qubits, we show that our method has practical importance since it provides a completely alternative route for measuring ensemble and quantum dephasing times, T2* and T2, using only repeated projective measurements and without the need for coherent spin control. Our approach is based on measuring time-correlators of a spin qubit in an optically active QD beyond the second order. We utilize a quantum dot spin-storage structure to initialize a single electron spin in a quantum dot subject to a magnetic field applied in Voigt geometry through tunnel ionization and perform repeated projective measurements of the spin at times t1 and t2. This measurement is repeated, corresponding to ensemble averaging, and the resulting third-order time correlations reveals rich physics: For times t1 or t2 < T2* Larmor precession is observed which reveals the ensemble dephasing time T2*. Importantly, even though the time-correlators were obtained through averaging many measurements for times t1 and t2 > T2* oscillations are observed that decay with the dephasing time T2 and allow its determination even without the need for coherent spin control. Finally, combining the third-order time correlator with the second-order time correlator allows to demonstrate a violation of Leggett-Garg type inequalities for certain times providing clear evidence for the quantum nature of the quantum dot spin. [1] A. Bechtold et al. Phys. Rev. Lett. 117, 027402 (2016)
We measure time correlators of a spin qubit in an optically active quantum dot beyond the second order. Such higher-order correlators are shown to be directly sensitive to pure quantum effects that cannot be explained within the classical framework. They allow direct determination of ensemble and quantum dephasing times, T_{2}^{*} and T_{2}, using only repeated projective measurements and without the need for coherent spin control. Our method enables studies of purely quantum behavior in solid state systems, including tests of the Leggett-Garg type of inequalities that rule out local hidden variable interpretation of the quantum-dot spin dynamics.
Abstract The correlations of fluctuations are key to studying fundamental quantum physics and quantum many‐body dynamics. They are also useful information for understanding and combating decoherence in quantum technology. Nonlinear spectroscopy and noise spectroscopy are powerful tools to characterize fluctuations, but they can access only very few among the many types of higher‐order correlations. A systematic quantum sensing approach, called quantum nonlinear spectroscopy (QNS), is recently proposed for extracting arbitrary types and orders of time‐ordered correlations, using sequential weak measurement via a spin quantum sensor. However, the requirement of a central spin as the quantum sensor limits the versatility of the QNS since usually a central spin interacts only with a small number of particles in proximity and the measurement of single spins needs stringent conditions. Here, the aim is to employ the polarization (a pseudo‐spin) of a coherent light beam as a quantum sensor for QNS. After interacting with a target system (such as a transparent magnetic material), the small Faraday rotation of the linearly polarized light can be measured, which constitutes a weak measurement of the magnetization in the target system. Using a Mach–Zehnder interferometer with a designed phase shift, one can post‐select the effects of the light–material interaction to be either a quantum evolution or a quantum measurement of the material magnetization. This way, the correlated difference photon counts of a certain number of measurement shots, each with a designated interference phase, can be made proportional to a certain type and order of correlations of the magnetic fluctuations in the material. The analysis of the signal‐to‐noise ratios shows that the second‐order correlations are detectable in general under realistic conditions and higher‐order correlations are significant when the correlation lengths of the fluctuations are comparable to the laser spot size (such as in systems near the critical points). Since the photon sensor can interact simultaneously with many particles and interferometry is a standard technique, this protocol of QNS is advantageous for studying quantum many‐body systems.
The theory of weak quantum measurements is developed for quantum-dot spin qubits. Building on recent experiments, we propose a control cycle to prepare, manipulate, weakly measure, and perform quantum state tomography. This is accomplished using a combination of the physics of electron spin resonance, spin blockade, and Coulomb blockade, resulting in a charge transport process. We investigate the influence of the surrounding nuclear spin environment, and find a regime where this environment significantly simplifies the dynamics of the weak-measurement process, making this theoretical proposal realistic with existing experimental technology. We further consider spin-echo refocusing to combat dephasing, as well as discuss a realization of ``quantum undemolition,'' whereby the effects of quantum state disturbance are undone.
Central spin decoherence is useful for detecting many-body physics in environments and moreover, the spin echo control can remove the effects of static thermal fluctuations so that the quantum fluctuations are revealed. The central spin decoherence approach, however, is feasible only in some special configurations and often requires uniform coupling between the central spin and individual spins in the baths, which are very challenging in experiments. Here, by making analogue between central spin decoherence and depolarization of photons, we propose a scheme of Faraday rotation echo spectroscopy (FRES) for studying quantum fluctuations in interacting spin systems. The echo control of the photon polarization is realized by flipping the polarization with a birefringence crystal. The FRES, similar to spin echo in magnetic resonance spectroscopy, can suppress the effects of the static magnetic fluctuations and therefore reveal dynamical magnetic fluctuations. We apply the scheme to a rare-earth compound LiHoF4 and calculate the echo signal, which is related to the quantum fluctuations of the system. We observe enhanced signals at the phase boundary. The FRES should be useful for studying quantum fluctuations in a broad range of spin systems, including cold atoms, quantum dots, solid-state impurities, and transparent magnetic materials.