Squeezed-light spin noise spectroscopy

Abstract

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...

Sensitivity, quantum limits, and quantum enhancement of noise spectroscopies

“…It is not a foregone conclusion that squeezing will help, however: in other applications of squeezed light to probe high-density ensembles [51], squeezing had no beneficial effect at the optimum. Using a sub-threshold OPO described in [34,38], we generate 2.6 dB of polarization squeezing, or ξ 2 = 0.55, and observe a reduction of Γ exp 22 and Γ exp 44 by a factor 0.61, constant to within uncertainties, as shown in Fig. 4.…”

“…As described in our previous work [34] the parameters v that appear in Eq. (4) have the following dependencies on (n, P ): S at ∝ P 2 n/∆ν, ∆ν = ∆ν 0 + An + BP , where A and B are constants describing collisional and power broadening, respectively, and S ph ∝ P ξ 2 , where ξ 2 is the squeezing parameter, with ξ 2 = 1 indicating the shot noise level.…”

“…For FR-SNS we show two new results concerning the quantum limits of the technique: first, availability of unlimited particle-number resources gives rise to an optimal sensitivity at finite number, in contrast to standard models from quantum metrology [36,37], which have sensitivity monotonic in particle number and thus must assume an externally-imposed constraint to give meaningful results, and second, the number-optimized standard-quantum-limit sensitivity can be surpassed using squeezed-light probes. These theoretical predictions are tested by comparison against FR-SNS of hot rubidium vapor using a quantum-noise-limited probing system [34] and atom-resonant optical squeezing [38,39]. The techniques demonstrated here enable a priori optimization of experimental conditions, to maximize the information obtained from noise spectra.…”

“…As described in the SI and in [34], v can be independently computed from the atomic number density n and probe power P , allowing first-principles computation of the covariance matrix Γ th through Eq. (3).…”

“…Non-optical SNS based on resonance force microscopy [19,20] Quantum statistical fluctuations such as shot noise are often limiting in noise spectroscopies [6,27,34], making it important to understand quantum limits and techniques to overcome them. A general framework to estimate the spectra of noisy classical forces influencing quantum systems has been applied to spectroscopy by homodyne detection of an externally-imposed noisy phase [35].…”