Spin-1 Atomic Condensate Research Articles

Detection of Entangled States Supported by Reinforcement Learning.

Discrimination of entangled states is an important element of quantum-enhanced metrology. This typically requires low-noise detection technology. Such a challenge can be circumvented by introducing nonlinear readout process. Traditionally, this is realized by reversing the very dynamics that generates the entangled state, which requires a full control over the system evolution. In this Letter, we present nonlinear readout of highly entangled states by employing reinforcement learning to manipulate the spin-mixing dynamics in a spin-1 atomic condensate. The reinforcement learning found results in driving the system toward an unstable fixed point, whereby the (to be sensed) phase perturbation is amplified by the subsequent spin-mixing dynamics. Working with a condensate of 10 900 ^{87}Rb atoms, we achieve a metrological gain of 6.97_{-1.38}^{+1.30} dB beyond the classical precision limit. Our work will open up new possibilities in unlocking the full potential of entanglement caused quantum enhancement in experiments.

Nonadiabatic quantum phase transition in a trapped spinor condensate

We study the effect of an external harmonic trapping potential on an outcome of the non-adiabatic quantum phase transition from an antiferromagnetic to a phase-separated state in a spin-1 atomic condensate. Previously, we demonstrated that the dynamics of an untrapped system exhibits double universality with two different scaling laws appearing due to conservation of magnetization. We show that in the presence of a trap double universality persists. However, the corresponding scaling exponents are strongly modified by transfer of local magnetization across the system. The values of these exponents cannot be explained by the effect of causality alone, as in the spinless case. We derive the appropriate scaling laws based on a slow diffusive-drift relaxation process in the local density approximation.

Using the ground state of an antiferromagnetic spin-1 atomic condensate for Heisenberg-limited metrology

We show that the ground state of a spin-1 atomic condensate with antiferromagnetic interactions constitutes a useful resource for quantum metrology upon approaching the Heisenberg limit. Unlike a ferromagnetic condensate state where individual atomic spins are aligned in the same direction, the antiferromagnetic ground-state condensate is a condensate of spin-singlet atom pairs. The inherent correlation between paired atoms allows for parameter estimation at precisions beyond the standard quantum limit (SQL) for uncorrelated atoms. The degree of improvement over the SQL is measured by the scaled quantum Fisher information (QFI), whose dependence on the ratio of linear Zeeman shift $p$ to spin-dependent atomic interaction $c$ is studied. At a typical value of $p=0.4c$, which corresponds to a magnetic field of $28.6\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{G}$ for $c=50\mathrm{h}$ Hz (for $^{23}\mathrm{Na}$ atom condensate in the $F=1$ state at a typical density of $\ensuremath{\sim}{10}^{14}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$), the scaled QFI can reach $\ensuremath{\sim}0.48N$, which approaches the limit of $0.5N$ for the twin-Fock state ${|N/2\ensuremath{\rangle}}_{+}{|N/2\ensuremath{\rangle}}_{\ensuremath{-}}$. Our work encourages experimental efforts to reach the ground state of an antiferromagnetic condensate at a extremely low magnetic field.

Atomic spin orbit coupling synthesized with gradient magnetic fields

Spin orbit coupling (SOC) for neutral atoms can be synthesized with pulsed or time modulating gradient magnetic field (GMF). This is confirmed through the studies of collective dipole oscillations for a spin-1 atomic condensate in a harmonic trap after abruptly turning on SOC and adiabatically adjusted equilibrium states when SOC strength is slowly ramped up. Further measurements reveal that SOC can be enhanced when the GMF modulation frequency approaches harmonic trap frequency. Additionally, we discuss how the technique of pulsed GMF can be used to synthesize space-period magnetic fields, or magnetic lattices.

Studies of atomic spin-orbit coupling synthesized with gradient magnetic fields

SynopsisAtomic spin orbit coupling (SOC) can be synthesized with modulating gradient magnetic field (GMF). This is confirmed through studying collective dipole oscillations for a spin-1 atomic condensate in a harmonic trap after abruptly turning on SOC, and studying adiabatically adjusted equilibrium states when SOC strength is slowly ramped up. Further measurements reveal that SOC can be enhanced when the GMF modulation frequency approaches trapping frequency.

Quantum spin mixing in a binary mixture of spin-1 atomic condensates

We study quantum spin mixing in a binary mixture of spin-1 condensates including coherent interspecies mixing process, using the familiar spinor condensates of $^{87}$Rb and $^{23}$Na atoms in the ground lower hyperfine F=1 manifolds as prototype examples. Within the single spatial mode approximation for each of the two spinor condensates, the mixing dynamics reduce to that of three coupled nonlinear pendulums with clear physical interpretations. Using suitably prepared initial states, it is possible to determine the interspecies singlet-pairing as well as spin-exchange interactions from the subsequent mixing dynamics.

Atomic-number fluctuations in a mixture of condensates

We study particle number fluctuations in the quantum ground states of a mixture of two spin-1 atomic condensates when the interspecies spin-exchange coupling interaction $c_{12}\beta$ is adjusted. The two spin-1 condensates forming the mixture are respectively ferromagnetic and polar in the absence of an external magnetic (B-) field. We categorize all possible ground states using the angular momentum algebra and compute their characteristic atom number fluctuations, focusing especially on the the AA phase (when $ c_{12}\beta >0$), where the ground state becomes fragmented and atomic number fluctuations exhibit drastically different features from a single stand alone spin-1 polar condensate. Our results are further supported by numerical simulations of the full quantum many-body system.

Spin-mixing dynamics in a spin-1 atomic condensate coupled with a molecular condensate

We study the coherent spin-mixing dynamics in a spin-1 atomic condensate coupled with a molecular condensate. A model is proposed to include the photoassociation (PA) interaction in a spinor condensate. If only the ${m}_{F}=\ensuremath{-}1$ spin component can be converted into molecules, the combined dynamics of spin-mixing and PA can be described by nonlinearly coupled pendulums. We performed detailed numerical calculations on the antiferromagnetic spin-1 systems. We find the spin-mixing dynamics can be greatly controlled by the PA field. The PA field can enhance or suppress the period and amplitude of the spin oscillations, which provide more degrees of freedom to control the spin-mixing dynamics.

Dynamical Instability and Domain Formation in a Spin-1 Bose-Einstein Condensate

We interpret the recently observed spatial domain formation in spin-1 atomic condensates as a result of dynamical instability. Within the mean field theory, a homogeneous condensate is dynamically unstable (stable) for ferromagnetic (antiferromagnetic) atomic interactions. We find that this dynamical instability naturally leads to spontaneous domain formation as observed in several recent experiments for condensates with rather small numbers of atoms. For trapped condensates, our numerical simulations compare quantitatively to the experimental results, thus largely confirming the physical insight from our analysis of the homogeneous case.

Coherent spin mixing dynamics in a spin-1 atomic condensate

We study the coherent off-equilibrium spin mixing inside an atomic condensate. Using mean field theory and adopting the single spatial mode approximation (SMA), the condensate spin dynamics is found to be well described by that of a nonrigid pendulum, and displays a variety of periodic oscillations in an external magnetic field. Our results illuminate several recent experimental observations and provide critical insights into the observation of coherent interaction-driven oscillations in a spin-1 condensate.

An effective quasi-one-dimensional description of a spin-1 atomic condensate

Within the mean field theory we extend the effective quasi-1D non-polynomial Schr\"{o}dinger equation (NPSE) approach to the description of a spin-1 atomic condensate in a tight radial confinement geometry for both weak and strong atom-atom interactions. Detailed comparisons with full time dependent 3D numerical simulations show excellent agreement as in the case of a single component scalar condensate, demonstrating our result as an efficient and effective tool for the understanding of spin-1 condensate dynamics observed in several recent experiments.