Amplification of fluctuations in a spinor Bose-Einstein condensate

Abstract

Dynamical instabilities due to spin-mixing collisions in a 87 Rb F = 1 spinor Bose-Einstein condensate are used as an amplifier of quantum spin fluctuations. We demonstrate the spectrum of this amplifier to be tunable, in quantitative agreement with mean-field calculations. We quantify the microscopic spin fluctuations of the initially paramagnetic condensate by applying this amplifier and measuring the resulting macroscopic magnetization. The magnitude of these fluctuations is consistent with predictions of a beyond-mean-field theory. The spinor-condensate-based spin amplifier is thus shown to be nearly quantum-limited at a gain as high as 30 dB.Accompanied by a precise theoretical framework and created in the lab in a highly controlled manner, ultracold atomic systems serve as a platform for studies of quantum dynamics and many-body quantum phases. Among these systems, gaseous spinor Bose Einstein condensates [1,2,3,4,5], in which atoms may explore all sub-levels of a non-zero hyperfine spin F , provide a compelling opportunity to access the static and dynamical properties of a magnetic superfluid [6,7,8,9,10].We previously identified a quantum phase transition in an F = 1 spinor Bose Einstein condensate between a paramagnetic and ferromagnetic phase [9]. This transition is crossed as the quadratic Zeeman energy term, of the form qF 2 z , is tuned through a critical value q = q 0 ; here, F z is the longitudinal (ẑ axis) projection of the dimensionless vector spin operator F. Accompanying this phase transition is the onset of a dynamical instability in a condensate prepared in the paramagnetic ground state, with macroscopic occupation of the |m z = 0 magnetic sublevel [11,12,13]. This instability causes transverse spin perturbations to grow exponentially, producing atoms into the |m z = ±1 sublevels. In contradiction with the mean-field prediction that the paramagnetic state should remain stationary because it lacks fluctuations by which to seed the instability, experiments revealed the spontaneous magnetization of such condensates after they were rapidly quenched across the phase transition.In this Letter, we investigate the spin fluctuations that become amplified by the spin-mixing instability. In particular, we test whether these fluctuations correspond to quantum noise, i.e. to the zero-point fluctuations of quantized spin excitation modes that become unstable. For this, we use the spin-mixing instability as an amplifier, evolving microscopic quantum fluctuations into measurable macroscopic magnetization patterns. We present two main results. First, we characterize the spin-mixing amplifier and demonstrate its spectrum to be tunable by varying the quadratic Zeeman shift. This spectrum compares well with a theoretical model that accounts for the inhomogeneous condensate density and for magnetic dipole interactions. Second, we measure precisely the transverse magnetization produced by this amplifier at various stages of amplification, up to a gain of 30 dB in the magnetization variance. This magnetization sig...

Long-time-scale dynamics of spin textures in a degenerateF=187Rb spinor Bose gas

“…The extinction of spin-mixing dynamics at negative q for condensates in the |m F = 0 states was observed previously [23].…”

“…In addition, the sample was exposed to a linearly polarized microwave-frequency magnetic field detuned by δ = ±2π × 40 kHz from the |F = 1,m F = 0 to |F = 2,m F = 0 hyperfine transition. The resulting ac Zeeman shift of q μ = −h 2 /4δ was used to tune the total quadratic shift q = q B + q μ by varying the Rabi frequency and by choosing the sign of δ [23,24].…”

Non-equilibrium dynamics of an unstable quantum pendulum explored in a spin-1 Bose–Einstein condensate

“…In particular, observation of coherent spin oscillations have confirmed the mean-field pendulum model for small condensates 4,9,10 . Spin evolution has been previously observed from metastable spin states in many experiments 6,8,[13][14][15][16][17] , however, the experiments have not yet demonstrated spin dynamic in agreement with quantum calculations, except in the perturbative, low-depletion limit at very short times (where a Bogoliubov expansion around the mean field can be used) 12,13,17 , or for conditions where the mean-field approach suffices. Here, we are able to observe quantum spin dynamics that agree well with quantum calculations and demonstrate a rich array of non-Gaussian fluctuations.…”

“…The equilibrium states, domain formation and spin dynamics of spinor condensates have been studied in many experiments [6][7][8][9][10][11][12][13][14][15][16][17] . In particular, observation of coherent spin oscillations have confirmed the mean-field pendulum model for small condensates 4,9,10 .…”

Parametric amplification of matter waves in dipolar spinor Bose-Einstein condensates

“…In that case, spin-changing collisions may lead to correlated Einstein-Podolsky-Rosen (EPR) pairs in m = ±1 [17,18], in a * fdeuretz@itp.uni-hannover.de process which closely resembles parametric down-conversion in nonlinear optics [19]. As a result, spinor condensates may act as parametric amplifiers of matter waves [20][21][22], opening interesting perspectives for the creation of nonclassical states of matter based on spinor BECs. Recently we have shown that the interplay between trapping potential, quadratic Zeeman effect (QZE), and spin-changing collisions crucially determines the amplification gain [21] and its sensitivity with respect to quantum spin fluctuations [22].…”