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arXiv:cond-mat/0601188

Quantum beat phenomenon presence in coherent spin dynamics of spin-2 $^{87}$Rb atoms in a deep optical lattice

Hua-Jun Huang, Guang-Ming Zhang

Published Jan 10, 2006• 1 citation
arXivHTMLPDF

Abstract

Motivated by the recent experimental work (A. Widera, \textit{et al}, Phys. Rev. Lett. 95, 19045), we study the collisional spin dynamics of two spin-2 $% ^{87}$Rb atoms confined in a deep optical lattice. When the system is initialized as $|0,0>$, three different two-particle Zeeman states are involved in the time evolution due to the conservation of magnetization. For a large magnetic field $B>0.8$ Guass, the spin coherent dynamics reduces to a Rabi-like oscillation between the states $|0,0>$ and $% |1,-1>$. However, under a small magnetic field, a general three-level coherent oscillation displays. In particular, around a critical magnetic field $B_{c}\simeq 0.48$ Guass, the probability in the Zeeman states $% |2,-2> $ exhibits a novel quantum beat phenomenon, ready to be confirmed in future experiments.

DOI
10.48550/arxiv.cond-mat/0601188

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Quantum beat phenomenon presence in coherent spin dynamics of spin-2 87^{87}87Rb atoms in a deep optical lattice
Motivated by the recent experimental work (A. Widera, \textit{et al}, Phys. Rev. Lett. 95, 19045), we study the collisional spin dynamics of two spin-2 % ^{87}Rb atoms confined in a deep optical lattice. When the system is initialized as ∣0,0>|0,0>∣0,0>, three different two-particle Zeeman states are involved in the time evolution due to the conservation of magnetization. For a large magnetic field B>0.8B>0.8B>0.8 Guass, the spin coherent dynamics reduces to a Rabi-like oscillation between the states ∣0,0>|0,0>∣0,0> and % |1,-1>. However, under a small magnetic field, a general three-level coherent oscillation displays. In particular, around a critical magnetic field Bc≃0.48B_{c}\simeq 0.48Bc​≃0.48 Guass, the probability in the Zeeman states % |2,-2> exhibits a novel quantum beat phenomenon, ready to be confirmed in future experiments.
We report on the observation of coherent, purely collisionally driven spin dynamics of neutral atoms in an optical lattice. For high lattice depths, atom pairs confined to the same lattice site show weakly damped Rabi-type oscillations between two-particle Zeeman states of equal magnetization, induced by spin-changing collisions. Moreover, measurement of the oscillation frequency allows for precise determination of the spin-changing collisional coupling strengths, which are directly related to fundamental scattering lengths describing interatomic collisions at ultracold temperatures.
We study the dynamics of spin-1 atoms in a periodic optical-lattice potential and an external magnetic field in a quantum quench scenario where we start from a superfluid ground state in a shallow lattice potential and suddenly raise the lattice depth. The time evolution of the nonequilibrium state shows collective collapse-and-revival oscillations of matter-wave coherence as well as oscillations in the spin populations. We show that the complex pattern of these two types of oscillations reveals details about the superfluid and magnetic properties of the initial many-body ground state. Furthermore, we show that the strengths of the spin-dependent and spin-independent atom-atom interactions can be deduced from the observations. The Hamiltonian that describes the physics of the final deep lattice not only contains two-body interactions but also effective multibody interactions, which arise due to virtual excitations to higher bands. We derive these effective spin-dependent three-body interaction parameters for spin-1 atoms and describe how spin mixing is affected. Spinor atoms are unique in the sense that multibody interactions are directly evident in the in situ number densities in addition to the momentum distributions. We treat both antiferromagnetic (e.g., 23{}^{23}23Na) and ferromagnetic (e.g., 87{}^{87}87Rb and 41{}^{41}41K) condensates.
We experimentally studied the spin-dependent collision dynamics of 87Rb^{87}\mathrm{Rb}87Rb spin-2 Bose-Einstein condensates confined in an optical trap. The condensed atoms were initially populated in the $\ensuremath{\mid}F=2,{m}_{F}=0⟩$ state, and their time evolutions in the trap were measured in the presence of external magnetic field strengths ranging from 0.1 to 3.0G3.0\phantom{\rule{0.3em}{0ex}}\mathrm{G}3.0G. The atom loss rate due to inelastic two-body collisions was found to be $1.4(2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{3}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. Spin mixing in the F=2F=2F=2 manifold developed dramatically for the first few tens of milliseconds, and the oscillations in the population distribution between different magnetic components were observed over a limited range of magnetic field strengths. The antiferromagnetic property of this system was deduced from the magnetic field dependence on the evolution of relative populations for each mF{m}_{F}mF​ component.
We demonstrate how the topological phase associated with Rabi flopping in two-level atoms in optical fields can be measured by quantum-beat experiments. We use the Zeeman coherences in j=0j=0j=0 to j=1j=1j=1 transition which is excited by both broad-band field and circularly polarized pulses.
Bose-Einstein condensation (BEC) is a phenomenon in which identical bosons occupy the same quantum state below a certain critical temperature. A hallmark of BEC is the coherence between particles every particle shares the same quantum wavefunction and phase. This coherence has been demonstrated for the external (motional) degrees of freedom of the atomic condensates by interfering two condensates. In this thesis, the coherence is shown to extend to the internal spin degrees of freedom of a spin-1 Bose gas evidenced by the observed coherent and reversible spin-changing collisions. The observed coherent dynamics are analogous to Josephson oscillations in weakly connected superconductors and represent a type of matter-wave four-wave mixing. Control of the coherent evolution of the system using magnetic fields is also demonstrated. The studies on spinor condensates begin by creating spinor condensates directly using all-optical approaches that were first developed in our laboratory. All-optical formation of Bose-Einstein condensates (BEC) in 1D optical lattice and single focus trap geometries are developed and presented. These techniques offer considerable flexibility and speed compared to magnetic trap approaches, and the trapping potential can be essentially spin-independent and are ideally suited for studying spinor condensates. Using condensates with well-defined initial non-equilibrium spin configuration, spin mixing of F = 1 and F = 2 spinor condensates of rubidium-87 atoms confined in an optical trap is observed. The equilibrium spin configuration in the F = 1 manifold confirms that 87Rb is ferromagnetic. The coherent spinor dynamics are demonstrated by initiating spin mixing deterministically with a non-stationary spin population configuration. Finally, the interplay between the coherent spin mixing and spatial dynamics in spin-1 condensates with ferromagnetic interactions is investigated.
We consider a quantum beat laser [Scully and Zubairy, Phys. Rev. A 35 752 (1987)] as a source of entangled radiation. The system essentially consists of three-level atoms inside a doubly resonant cavity such that coherence is introduced by driving the upper two levels with a strong classical field of Rabi frequency $\ensuremath{\Omega}$. We study the dynamics of this system for different values of Rabi frequencies in the presence of cavity losses. It is shown that entanglement can be generated in this system for different initial states of the field in the two modes.