Spin Noise Spectroscopy Beyond Thermal Equilibrium and Linear Response

P. Glasenapp, N. A. Sinitsyn, Luyi Yang, D. G. Rickel, D. Roy, A. Greilich, M. Bayer, and S. A. Crooker

Phys. Rev. Lett. 113, 156601 – Published 6 October 2014

Abstract

Per the fluctuation-dissipation theorem, the information obtained from spin fluctuation studies in thermal equilibrium is necessarily constrained by the system’s linear response functions. However, by including weak radio frequency magnetic fields, we demonstrate that intrinsic and random spin fluctuations even in strictly unpolarized ensembles can reveal underlying patterns of correlation and coupling beyond linear response, and can be used to study nonequilibrium and even multiphoton coherent spin phenomena. We demonstrate this capability in a classical vapor of ${}^{41}K$ alkali atoms, where spin fluctuations alone directly reveal Rabi splittings, the formation of Mollow triplets and Autler-Townes doublets, ac Zeeman shifts, and even nonlinear multiphoton coherences.

Received 7 July 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.156601

Authors & Affiliations

P. Glasenapp¹, N. A. Sinitsyn², Luyi Yang³, D. G. Rickel³, D. Roy², A. Greilich¹, M. Bayer¹, and S. A. Crooker³

¹Experimentelle Physik 2, Technische Universität Dortmund, D-44221 Dortmund, Germany
²Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
³National High Magnetic Field Lab, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

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Vol. 113, Iss. 15 — 10 October 2014

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Images

Figure 1
(a) Experimental schematic. Random spin fluctuations $δ S_{z} (t)$ in ${}^{41}K$ vapor impart Faraday rotation fluctuations $δ θ_{F} (t)$ on the probe laser, which are detected by balanced photodiodes. The probe laser is detuned by $\sim 40 GHz$ from the ${}^{41}K$ $D 1$ transition ( $λ = 770.1 nm$ ). A static transverse magnetic field $B_{dc}$ is applied along $\hat{y}$ , and a tunable radio-frequency field $| B_{ac} | \sin (ω_{ac} t)$ can be applied along $\hat{x}$ . (b) Equilibrium spin noise spectrum from ${}^{41}K$ ( $T = 185 ° C$ , $B_{dc} \approx 11 G$ , $| B_{ac} | = 0$ ). Noise peaks arise from spontaneous (fluctuation-induced) spin coherences between neighboring $Δ F = 0$ , $Δ m_{F} = \pm 1$ Zeeman sublevels in the ${}^{41}K$ ground state (see inset). (c) A plot of the ${}^{41}K$ spin noise spectra as $ω_{ac}$ is swept through the Zeeman coherences ( $| B_{ac} | \sim 0.1 G$ ). The induced Rabi splittings, Mollow triplets, and Autler-Townes doublets are all revealed by the intrinsic spin noise. $⟨ S_{z} (t) ⟩ = 0$ throughout the measurement.
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Figure 2
(a) ${}^{41}K$ spin noise spectrum when $B_{ac}$ is resonant with the lowest-energy Zeeman coherence $a$ ( $ω_{ac} = ω_{a}$ ). (b) Noise spectrum when $B_{ac}$ resonant with the degenerate coherences $b$ and $f$ . Diagrams show the Rabi splittings of the relevant Zeeman sublevels, and all allowed transitions, which show up clearly in the spin noise. Red and blue arrows indicate the Mollow triplet and the Autler-Townes doublet transitions, respectively; black arrows indicate unperturbed coherences. (Note that for these spectra $ω_{ac}$ was fixed; specific coherences were tuned into resonance by adjusting $B_{dc}$ .)
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Figure 3
${}^{41}K$ spin noise spectra in the presence of a nonresonant $B_{ac}$ . $ω_{ac} = \frac{1}{2} (ω_{b} + ω_{c})$ , $B_{dc} \approx 13 G$ . ac Zeeman shifts ( $\propto | B_{ac} |^{2}$ ) of all noise coherences are evident. Dotted lines show expected ac Zeeman shifts computed to lowest order. Additional splittings of the spin noise peaks emerge at large $| B_{ac} |$ , due to higher-order multiphoton coupling (see text).
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Figure 4
(a) Diagram showing the upper three Zeeman sublevels ( $m_{F} = 2$ ,1,0) of the ${}^{41}K$ $F = 2$ manifold, in the “dressed state” picture, versus rf photon energy $ℏ ω_{ac}$ . Uncoupled states are labeled by $| m_{F}, # photons ⟩$ and appear as dashed straight lines. Solid curved lines show the new coupled states that anticross. Mollow triplet (red arrows) and Autler-Townes doublet transitions (blue) are indicated. A higher-order (two-photon) anticrossing is shown at the right. (b) The measured doublet splitting is linear (quadratic) in $| B_{ac} |$ for the case of one- (two-) photon anticrossing.
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