Parametric Amplification of Vacuum Fluctuations in a Spinor Condensate

Abstract

Parametric amplification of vacuum fluctuations is crucial in modern quantum optics, enabling the creation of squeezing and entanglement. We demonstrate the parametric amplification of vacuum fluctuations for matter waves using a spinor F = 2 87 Rb condensate. Interatomic interactions lead to correlated pair creation in the mF = ±1 states from an initial unstable mF = 0 condensate, which acts as a vacuum for mF = 0. Although this pair creation from a pure mF = 0 condensate is ideally triggered by vacuum fluctuations, unavoidable spurious initial mF = ±1 atoms induce a classical seed which may become the dominant triggering mechanism. We show that pair creation is insensitive to a classical seed for sufficiently large magnetic fields, demonstrating the dominant role of vacuum fluctuations. The presented system thus provides a direct path towards the generation of non-classical states of matter on the basis of spinor condensates.Parametric amplification of vacuum fluctuations in nonlinear media [1] plays a crucial role in the investigation and application of non-classical states of light. These states have revolutionized the field of quantum optics in the past decades. Since the first observation of squeezed light [2], these non-classical states of light have become a valuable tool in modern optics, e.g. for the enhancement of modern interferometers [3]. Similarly, the production of entangled photon pairs [4] has triggered an ongoing series of fundamental tests of modern quantum mechanics [5,6] and has many possible applications for quantum computing [7]. The tools developed for the production and manipulation of ultracold neutral atoms now bring many of these seminal investigations within the scope of experiments with matter waves. In this sense, the production of number-squeezed Bose-Einstein condensates (BECs) [8] and spin squeezed thermal clouds [9] has been recently demonstrated.Spinor BECs, consisting of atoms with non-zero spin F , provide an optimal non-linear medium for the production of non-classical states of matter. In these systems, inter-particle interactions lead to a coherent population transfer between different Zeeman m F sublevels (spin dynamics). The case of a sample prepared in m F = 0 (represented by |0 ) is particularly interesting. In that case the initial stages of the spin dynamics are characterized by the production of correlated atom pairs in |±1 [10,11], resembling the production of EinsteinPodolsky-Rosen (EPR) pairs in optical parametric down conversion [5].Ideally a pure initial |0 BEC acts as a vacuum for atoms in m F = 0. Hence pair creation into |±1 can be understood as a parametric amplification of quantum vacuum fluctuations. However, parametric amplifiers are exponentially sensitive to any spurious initial seed in the amplified modes, which may easily dominate the effect of vacuum fluctuations. Despite careful purification proce-0

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

“…Interestingly, this process resembles parametric down-conversion in optical parametric amplifiers [19]. Indeed, if the m = 0 BEC is unstable after the quench of q, spinchanging collisions lead to an exponential amplification of the population in m = ±1 [20][21][22].…”

“…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].…”

“…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].…”