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arXiv:2008.10071 · Physical Review A

Laser control of the singlet-pairing process in an ultracold spinor mixture

Jianwen Jie, Yonghong Yu, Dajun Wang, Peng Zhang

Published May 25, 2021• 4 citations
arXivHTMLPDF

Abstract

In the mixture of ultracold spin-1 atoms of two different species A and B (e.g., $^{23}\mathrm{Na}$ (A) and $^{87}\mathrm{Rb}$ (B)), the interspecies singlet-pairing process ${\mathrm{A}}_{+1}+{\mathrm{B}}_{\ensuremath{-}1}\ensuremath{\rightleftharpoons}{\mathrm{A}}_{\ensuremath{-}1}+{\mathrm{B}}_{+1}$ can be induced by the spin-dependent interatomic interaction, where subscript $\ifmmode\pm\else\textpm\fi{}1$ denotes the magnetic quantum number. Nevertheless, one cannot isolate this process from other spin-changing processes, which are usually much stronger, by tuning the bias real magnetic field. As a result, it is difficult to clearly observe the singlet-pairing process and precisely measure the corresponding interaction strength. In this work we propose to control the singlet-pairing process via combining the real magnetic field and a laser-induced species-dependent synthetic magnetic field. With our approach one can significantly enhance this process and simultaneously suppress all other spin-changing processes. We illustrate our approach for both a confined two-atom system and a binary mixture of spinor Bose-Einstein condensates. Our control scheme is helpful for the precise measurement of the weak singlet-pairing interaction strength and the entanglement generation of two different atoms.

DOI
10.1103/physreva.103.053321

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In the mixture of ultracold spin-1 atoms of two different species A and B (e.g., 23Na^{23}\mathrm{Na}23Na (A) and 87Rb^{87}\mathrm{Rb}87Rb (B)), the interspecies singlet-pairing process A+1+B\ensuremath−1\ensuremath⇌A\ensuremath−1+B+1{\mathrm{A}}_{+1}+{\mathrm{B}}_{\ensuremath{-}1}\ensuremath{\rightleftharpoons}{\mathrm{A}}_{\ensuremath{-}1}+{\mathrm{B}}_{+1}A+1​+B\ensuremath−1​\ensuremath⇌A\ensuremath−1​+B+1​ can be induced by the spin-dependent interatomic interaction, where subscript \ifmmode±\else\textpm\fi1\ifmmode\pm\else\textpm\fi{}1\ifmmode±\else\textpm\fi1 denotes the magnetic quantum number. Nevertheless, one cannot isolate this process from other spin-changing processes, which are usually much stronger, by tuning the bias real magnetic field. As a result, it is difficult to clearly observe the singlet-pairing process and precisely measure the corresponding interaction strength. In this work we propose to control the singlet-pairing process via combining the real magnetic field and a laser-induced species-dependent synthetic magnetic field. With our approach one can significantly enhance this process and simultaneously suppress all other spin-changing processes. We illustrate our approach for both a confined two-atom system and a binary mixture of spinor Bose-Einstein condensates. Our control scheme is helpful for the precise measurement of the weak singlet-pairing interaction strength and the entanglement generation of two different atoms.
We study the ground-state properties of a mixture formed by two spin-1 condensates in the absence of an external magnetic field. As the collisional symmetry between interspecies bosonic atoms is broken, the interspecies coupling interaction ($\ensuremath{\beta}$) and interspecies singlet-pairing interaction ($\ensuremath{\gamma}$) arise. The ground state can be calculated using the angular momentum theory analytically for $\ensuremath{\gamma}=0$. The full quantum approach of exact diagonalization is adopted numerically to consider the more general case as $\ensuremath{\gamma}\ensuremath{\ne}0$. We illustrate the competition between the two interspecies interactions and find that as singlet-pairing interaction dominates (or the total spin vanishes), there are still different types of singlet formations which are well determined by $\ensuremath{\beta}$.
We report the observation of coherent heteronuclear spin dynamics driven by interspecies spin-spin interaction in an ultracold spinor mixture, which manifests as periodical and well-correlated spin oscillations between two atomic species. In particular, we investigate the magnetic field dependence of the oscillations and find a resonance behavior which depends on both the linear and quadratic Zeeman effects and the spin-dependent interaction. We also demonstrate a unique knob for controlling the spin dynamics in the spinor mixture with species-dependent vector light shifts.
We study the ground state and classify its phase diagram for a mixture of two spin-1 condensates in the absence of an external magnetic (B)(B)(B) field according to atomic parameters for intra- and interspecies spin-exchange coupling and singlet-pairing interaction. Ignoring the interspecies singlet-pairing interaction, the ground-state phases are found analytically. A numerical approach of simulated annealing is adopted when the singlet-pairing interaction is present. Our results on the phase diagram and the boundaries between phases allow for easy identifications of quantum phase transitions, which can be induced through the tuning of optical traps and atom numbers. They provide insight and guidance for several ongoing experiments on mixtures of spinor condensates.
This thesis reports on the first observation of optical tuning of interactions in an ultracold atomic gas. To control the elastic interactions, we use optically induced scattering resonances. They are realized by coupling pairs of atoms to a bound molecular state with the help of laser light. In comparison to the well-known magnetic Feshbach resonances, these optical Feshbach resonances allow a very fast switching of interactions in a spatially resolved way. This is because laser light can be switched on and off much faster than magnetic fields and because the light intensity can be spatially structured. Our experiments are performed with a Bose-Einstein condensate (BEC) of Rb atoms, which we produce in our new BEC setup. This apparatus has been constructed in the framework of this thesis and offers excellent optical access to the ultracold atom cloud. To investigate the tunability of atomic interactions with single-frequency laser light, we optically couple pairs of free atoms to an electronically excited molecular state. The coupling is achieved with a laser that is tuned close to the respective free-bound photoassociation transition. By changing the laser detuning we are able to adjust the atomic scattering length to any value between 10 a0 and 190 a0, where a0 denotes the Bohr radius. The atomic scattering length is a single quantity that fully describes ultracold elastic interactions. Since laser induced atom losses restrict the duration of our experiments, Bragg spectroscopy is employed as a fast method to measure the scattering length. We also demonstrate that optical Feshbach resonances can be realized with a two-color Raman coupling scheme. To implement this scheme, a second laser is added that couples the excited molecular state to a weakly bound molecular level in a ground state potential. Tuning the second laser results in a modification of the atomic scattering length similar to the one observed with a single laser. In addition, this scheme allows to control the width of the resonance via the detuning of the first laser. For the one-color and two-color coupling schemes, we investigate how the elastic scattering properties depend on the different available parameters, i.e. the laser detunings and intensities. Our experimental findings can successfully be described with an available theoretical model, which treats ultracold collisions in the presence of laser light. Optical Feshbach resonances have the possibility of becoming a valuable tool for fast switching of interactions. This is of special interest in quantum computation schemes with neutral atoms, where interactions between different atomic qubits need to be controlled.
We study quantum spin mixing in a mixture of two spin-1 condensates including coherent interspecies mixing processes, using condensates of 87{}^{87}87Rb and 23{}^{23}23Na atoms in the ground lower hyperfine F=1F=1F=1 manifold as prototype examples. Adopting the single spatial mode approximation for each of the two spinor condensates, we find the mixing dynamics reduce to that of three coupled nonrigid pendulums with clear physical interpretation. With suitably prepared initial states, the spin mixing dynamics allow for the determination of interspecies singlet-pairing as well as spin-exchange interaction parameters.
Spinor Bose-Einstein condensates (BECs) are multi-component superfluids with magnetic interactions, formed from dilute gases of atoms in the Zeeman sublevels mF of a single hyperfine ground state F. Spinor BECs are inherently magnetic quantum objects, and exhibit a multitude of features such as spin domains, magnon excitations, and distinct magnetic phases. At the heart of the magnetic nature of a spinor BEC is the spin-dependent collisional interaction c, which determines the overall magnetic behaviour of the superfluid. In conjunction with the quadratic Zeeman shift q, the magnitude and sign of c give rise to an intricate magnetic phase diagram. The magnetic phase of a spinor BEC is tunable, and c and q are the knobs. In addition to realising quantum simulators of magnetism, spinor BECs are also precise magnetic sensors. Atomic magnetometry measures the Larmor precession frequency of atoms, which is proportional to the magnetic field strength. The sensitivity of an atomic magnetometer is principally dependent on the duration of the measurement (interrogation time) and number of atoms participating in the measurement. BECs are highly suitable as atomic magnetometers, allowing for long interrogation times and high atomic density, with microscopic sensor volumes. The latter is an important consideration, as measurement of small magnetic sources demand equally microscopic sensors. Established forms of magnetometry (such as warm vapour magnetometers) use large sensing volumes and are not trivially miniaturised. The exquisite sensitivity of a spinor BEC to magnetic fields becomes a liability when one studies low energy (~ 1 Hz) spinor physics over long evolution times (100 ms) in a typical laboratory environment. To first order, the spin-collisional interaction is independent of the magnetic field. However, spatially inhomogeneous magnetic fields are problematic, exerting mechanical forces on the magnetically sensitive spin components, suppressing spin collisions and possibly introducing relaxation mechanisms that confound the observation of intrinsic equilibration. Precise characterisation of magnetic field gradients and their cancellation is thus of paramount importance. In this thesis, the interaction of a spinor BEC with its environment is studied. The construction, operation and optimisation of a BEC machine is described in detail, as well as the quantum state preparation and control techniques used. Spin-mixing collisions were studied by observing population oscillations, the characteristic hallmark of such coherent phenomena. The observed population dynamics showed strong evidence of the deleterious effects of magnetic field gradients. A series of experiments were performed using spin-echo pulse sequences to decouple the evolving spinor condensate from the inhomogeneous magnetic environment with encouraging results, but which posed further questions. The fidelity of spin-echo pulses in the strong radiative coupling regime was also studied. Spinor condensates were then employed as sensitive magnetometers to characterise the magnetic landscape they inhabit. A new method of measuring magnetic field gradients was developed, using a pair of spinor BECs separated in space that are simultaneously addressed by a Ramsey interferometry sequence. Combined with a re-orientable magnetic bias field, the resulting gradiometer was used to measure the magnetic field gradient tensor in vacuo. This scheme can be extended to realise a high-precision vector co-magnetometer, with spatiotemporal sensitivity comparable to established forms of magnetometry. Vector light shifts (VLSs) are optically-induced energy shifts that result in effective magnetic fields, which in our case originate from the laser beams used to trap the atoms. The VLS vanishes for purely linearly polarised light, which is experimentally difficult to obtain in vacuo. Small elliptical polarisation imperfections originating from birefringent optics and the glass vacuum cell result in a non-zero shift that contaminates magnetometry measurements. The VLS is spatially varying due to the intensity gradient of the trapping light. Due to gravitational sag of the trapping potential, the spatial variation of the VLS is accentuated, resulting in an effective magnetic field gradient that contributes to dephasing and component separation. The simultaneous Ramsey interferometry experiments are then adapted to measure the VLS-induced Zeeman shift and diagnose its elimination. Up to 99.96% of the VLS is eliminated using this method, and extensions to the technique are described.