Two-colour spin noise spectroscopy and fluctuation correlations reveal homogeneous linewidths within quantum-dot ensembles

Yang, Luyi; Glasenapp, Ph.; Greilich, A.; Reuter, D.; Wieck, A. D.; Yakovlev, D. R.; Bayer, М.; Crooker, S. A.

doi:10.1038/ncomms5949

Cited by 65 publications

(68 citation statements)

References 35 publications

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“…SNS has allowed measurement of g-factors, nuclear spin, isotope abundance ratios and relaxation rates of alkali atoms [5,6], g-factors, relaxation times and doping concentration of electrons in semiconductors [7][8][9][10][11] and localized holes in quantum dot ensembles [12,13] including single hole spin detection [14]. Recently, SNS has been used to study complex optical transitions and broadening processes [15,16], coherent phenomena beyond linear response [17] and cross-correlations of heterogeneous spin systems [18,19].Spin noise has been measured with nuclear magnetic resonance [20,21] and magnetic force microscopy [22][23][24], but the most sensitive and widely used detection technique is Faraday rotation (FR) [2,5,6], in which the spin noise is mapped onto the polarization of an off-resonant probe. In FR-SNS, spin noise near the Larmor frequency competes with quantum noise [25] of the detected photons, i.e., the optical shot noise.…”

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Squeezed-light spin noise spectroscopy

et al. 2016

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We report quantum enhancement of Faraday rotation spin noise spectroscopy by polarization squeezing of the probe beam. Using natural abundance Rb in 100 Torr of N2 buffer gas, and squeezed light from a sub-threshold optical parametric oscillator stabilized 20 GHz to the blue of the D1 resonance, we observe that an input squeezing of 3.0 dB improves the signal-to-noise ratio by 1.5 dB to 2.6 dB over the combined (power)⊗(number density) ranges (0.5 mW to 4.0 mW)⊗(1.5 ×10 12 cm −3 to 1.3 ×10 13 cm −3 ), covering the ranges used in optimized spin noise spectroscopy experiments. We also show that squeezing improves the trade-off between statistical sensitivity and broadening effects, a previously unobserved quantum advantage.The presence of intrinsic fluctuations of a spin system in thermal equilibrium was first predicted by Bloch [1] and experimentally demonstrated in the 1980's by Aleksandrov and Zapasskii [2]. In the last decade, "spin noise spectroscopy" (SNS) has emerged as a powerful technique for determining physical properties of an unperturbed spin system from its noise power spectrum [3,4]. SNS has allowed measurement of g-factors, nuclear spin, isotope abundance ratios and relaxation rates of alkali atoms [5,6], g-factors, relaxation times and doping concentration of electrons in semiconductors [7][8][9][10][11] and localized holes in quantum dot ensembles [12,13] including single hole spin detection [14]. Recently, SNS has been used to study complex optical transitions and broadening processes [15,16], coherent phenomena beyond linear response [17] and cross-correlations of heterogeneous spin systems [18,19].Spin noise has been measured with nuclear magnetic resonance [20,21] and magnetic force microscopy [22][23][24], but the most sensitive and widely used detection technique is Faraday rotation (FR) [2,5,6], in which the spin noise is mapped onto the polarization of an off-resonant probe. In FR-SNS, spin noise near the Larmor frequency competes with quantum noise [25] of the detected photons, i.e., the optical shot noise. The main figure of merit is η, the peak power spectral density (PSD) due to spin noise over the PSD due to shot noise, called "signal strength" [26] or the "signal-to-noise ratio" (SNR). Reported SNR for single-pass atomic ensembles ranges from 0 dB to 13 dB [5,27], and up to 21 dB in atomic multi-pass cells [28]. Due to weaker coupling to the probe beam, reported SNR ranges from −50 dB to −20 dB in semiconductor systems (See Table 1 in [26]). Several works have studied how to improve the polarimetric sensitivity [29] or to cancel technical noise sources [7,8,10], but without altering the fundamental tradeoff between sensitivity and broadening processes [29].For small optical power P and atomic density n, SNR is linear in each: η ∝ nP . At higher values, light scattering and atomic collisions broaden the spin noise resonances, and thus introduce systematic errors in measurements, e.g. of relaxation rates, that are derived from the SNS linewidth [5][6][7]. This trade-off between statis...

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Squeezed-light spin noise spectroscopy

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“…Interaction effects between spins of a single species in a sample can also be determined by two-beam SNS when the two probe laser beams are spatially separated as shown in Fig. 1(a) [39,41]. Thus, we propose that the two-beam SNS measurements can be used to separate the MBL phase from an AL phase.…”

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“…SNS with a single probe laser has been useful in characterizing various properties (e.g., g-factors, relaxation rates and decoherence times) of different spin ensembles, such as specific alkali atoms [30], itinerant electron spins in semiconductors [33] and localized hole spins in quantum dot ensembles [34]. Last year, an extension of the traditional SNS has been proposed and demonstrated by using two linearly polarized probe lasers for detecting inter-species spin interactions in a heterogeneous twocomponent spin ensemble interacting via binary exchange coupling in thermal equilibrium [39,40]. In this crosscorrelation SNS method, intrinsic spin fluctuations from two different species are independently detected, and interaction effects are determined by the cross-correlation of these two spin noise signals.…”

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Probing many-body localization by spin noise spectroscopy

2015

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We propose to apply spin noise spectroscopy (SNS) to detect many-body localization (MBL) in disordered spin systems. The SNS methods are relatively non-invasive technique to probe spontaneous spin fluctuations. We here show that the spin noise signals obtained by cross-correlation SNS with two probe beams can be used to separate the MBL phase from a noninteracting Anderson localized phase and a delocalized (diffusive) phase in the studied models for which we numerically calculate real time spin noise signals and their power spectra. For the archetypical case of the disordered XXZ spin chain we also develop a simple phenomenological model.The fate of Anderson localization in the presence of inter-particle interactions in a disordered quantum medium is an exciting frontier in condensed matter physics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. It is well known that all states of a onedimensional (1D) disordered chain of noninteracting particles are Anderson localized (AL) for any amount of disorder [20,21]. Thus, the AL state is a perfect insulator as long as the particles are not coupled to other degrees of freedom. In the presence of inter-particle interactions, a dynamical transition from a delocalized (diffusive) phase to a many-body localized (MBL) phase has been predicted in disordered quantum media when the strength of (quenched) randomness is increased [4][5][6][7][8][9].The MBL state is also a perfect insulator, but it has different dynamical properties compared to the AL state of noninteracting particles [10][11][12]16]. For example, entanglement entropy in the MBL phase shows a slow logarithmic growth following a global quench in an isolated system [10][11][12]. However, the entanglement entropy is very difficult to measure experimentally, and electrons or spins in conventional solid-state systems are coupled to an environment such as a phonon bath. Recent studies show that signatures of the MBL phase can survive in the presence of weak coupling to a thermalizing environment [22,23]. In particular, the spectral functions of local operators can be used to identify the MBL phase in the presence of weak dissipation [22,23].A new experimental approach based on a modified nonlocal spin-echo protocol along with a double electronelectron resonance technique in electron spin resonance has been proposed to distinguish the MBL phase from a noninteracting AL phase and a delocalized phase at infinite temperature [24]. The proposed approach can probe interaction effects, thus is able to separate the MBL phase from the AL phase. The method does involve optical pumping or polarization of local spins by external pulse fields, which can in principle lead to unwanted local heating and excitations. Here we propose a relatively non-invasive method based on spin noise spectroscopy (SNS) to distinguish the MBL phase from the AL phase and the delocalized phase in disordered spin systems.The optical SNS method has been developed recently as an alternative to conventional perturbation-based (pump-probe)...

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“…Techniques such as four-wave mixing and spectral hole-burning are used in optical spectroscopy [1][2][3] , and spin-echo 4 in nuclear magnetic resonance (NMR). However, the high-power pulses used in spin-echo and other sequences [4][5][6][7][8] often create spurious dynamics 7,8 obscuring the subtle spin correlations important for quantum technologies 5,6,9-17 .…”

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Few-second-long correlation times in a quantum dot nuclear spin bath probed by frequency-comb nuclear magnetic resonance spectroscopy

et al. 2016

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One of the key challenges in spectroscopy is the inhomogeneous broadening that masks the homogeneous spectral lineshape and the underlying coherent dynamics. Techniques such as four-wave mixing and spectral hole-burning are used in optical spectroscopy [1][2][3] , and spin-echo 4 in nuclear magnetic resonance (NMR). However, the high-power pulses used in spin-echo and other sequences [4][5][6][7][8] often create spurious dynamics 7,8 obscuring the subtle spin correlations important for quantum technologies 5,6,9-17 . Here we develop NMR techniques to probe the correlation times of the fluctuations in a nuclear spin bath of individual quantum dots, using frequency-comb excitation, allowing for the homogeneous NMR lineshapes to be measured without high-power pulses. We find nuclear spin correlation times exceeding one second in self-assembled InGaAs quantum dots-four orders of magnitude longer than in strain-free III-V semiconductors. This observed freezing of the nuclear spin fluctuations suggests ways of designing quantum dot spin qubits with a well-understood, highly stable nuclear spin bath.Pulsed magnetic resonance is a diverse toolkit with applications in chemistry, biology and physics. In quantum information applications, solid state spin qubits are of great interest and are often described by the so-called central spin model, where the qubit (central spin) is coupled to a fluctuating spin bath (typically interacting nuclear spins). Here microwave and radiofrequency (rf) magnetic resonance pulses are used for the initialization and readout of a qubit 18 , dynamical decoupling 5 and dynamic control 6 of the spin bath.However, the most important parameter controlling the central spin coherence 9,11,19 -the correlation time τ c of the spin bath fluctuations-is very difficult to measure directly. The value of τ c is determined by the spin exchange (flip-flops) of the interacting nuclear bath spins. By contrast, pulsed NMR reveals the spin bath coherence time T 2 , which characterizes the dynamics of the transverse nuclear magnetization 7,8,20 and is much shorter than τ c . The problem is further exacerbated in self-assembled quantum dots, where quadrupolar effects lead to inhomogeneous NMR broadening exceeding 10 MHz (refs 21,22), so that pulsed NMR requires practically unattainable rf field amplitudes exceeding 1 T.Here we develop an alternative approach to NMR spectroscopy: we measure non-coherent depolarization of nuclear spins under weak noise-like rf fields. Contrary to intuitive expectation, we show that such measurement can reveal the full homogeneous NMR lineshape describing the coherent spin dynamics. This is achieved by employing rf excitation with a frequency-comb profile (widely used in precision optical metrology 23 ). We then exploit non-resonant nuclear-nuclear interactions: the homogeneous NMR lineshape of one isotope measured with frequency-comb NMR is used as a sensitive non-invasive probe of the correlation times τ c of the nuclear flip-flops of the other isotope. Although initial studies 9,1...

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Two-colour spin noise spectroscopy and fluctuation correlations reveal homogeneous linewidths within quantum-dot ensembles

Cited by 65 publications

References 35 publications

Squeezed-light spin noise spectroscopy

Squeezed-light spin noise spectroscopy

Probing many-body localization by spin noise spectroscopy

Few-second-long correlation times in a quantum dot nuclear spin bath probed by frequency-comb nuclear magnetic resonance spectroscopy

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