Semiconductor spin noise spectroscopy: Fundamentals, accomplishments, and challenges

Müller, G.; Oestreich, M.; Römer, Michael; Hübner, Jens

doi:10.1016/j.physe.2010.08.010

Cited by 125 publications

(133 citation statements)

References 203 publications

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“…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].…”

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“…Theory -As described in detail in the Appendix, FR optical probing gives a signal proportional to the on-axis projection of the collective spin of a group of atoms in thermal equilibrium. The collective spin precesses in response to external magnetic fields and experiences a stochastic motion as required by the fluctuationdissipation theorem [2,26]. For rubidium, which has two isotopes 85 Rb and 87 Rb, and shot-noise limited detection [34], the power spectrum of the FR signal is given by a double Lorentzian function:…”

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“…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].…”

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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

et al. 2016

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“…The recent progress in the area of digital high-speed spectrum analyzers of electric signals gave rise to a strong increase of the interest to the optical noise spectroscopy [1,2,3,4,5,6]. In the first experimental observation of EPR of sodium atoms in the Faraday rotation noise spectrum [7], a high polarimetric sensitivity [8] made it possible to detect the above spectrum using a conventional lock-in amplifier.…”

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Noise spectroscopy of an optical microresonator

Kozlov

2013

J. Exp. Theor. Phys.

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The intensity noise spectrum of the light passed through an optical microcavity is calculated with allowance for thermal fluctuations of its thickness. The spectrum thus obtained reveals a peak at the frequency of acoustic mode localized inside the microcavity and depends on the size of the illuminated area. The estimates of the noise magnitude show that it can be detected using the up-to-date noise spectroscopy technique.

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“…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) techniques for measuring dynamical spin properties [25,26]. Intrinsic spin fluctuations of electrons and holes are passively detected in SNS by measuring optical Faraday rotation fluctuations of a linearly polarized probe laser beam passing through the sample [27][28][29][30][31][32][33][34][35][36][37][38].…”

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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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Semiconductor spin noise spectroscopy: Fundamentals, accomplishments, and challenges

Cited by 125 publications

References 203 publications

Squeezed-light spin noise spectroscopy

Squeezed-light spin noise spectroscopy

Noise spectroscopy of an optical microresonator

Probing many-body localization by spin noise spectroscopy

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