First Demonstration of Spin-Orbit Coupling in Ultracold Fermi Gases
Photo: Jing Zhang of Shanxi University
Authors: Hui Zhai1 and Jing Zhang2
1Institute for Advanced Study, Tsinghua University, Beijing, China
2State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan, China
Photo: Hui Zhai of Tsinghua University
In 1995, scientists successfully cooled bosons to Bose-Einstein condensate, and later on in 1999, quantum degenerate Fermi gas could also be demonstrated in experiment. These degenerate atomic gases have the advantage that both their single particle motion and the interaction between atoms can be manipulated and well controlled by light or magnetic field. Utilizing these advantages -- during the last decade -- many exciting experiments have been carried out, which either simulate interesting models for condensed matter systems or reveal interesting new many-body quantum phases or quantum phenomena.
However, in all these studies, an important ingredient has not been included until very recently, that is, the coupling between the atomic spin degree of freedom and its orbital motion. This is because for neutral atoms, unlike charged electrons, there is no intrinsic spin-orbit coupling. Nevertheless, in reality, spin-orbit coupling plays a very important role in determining electron structure in solid and the nuclear structure. Spin-orbit coupling is also the key ingredient giving birth to some new states of matters such as topological insulators and topological superfluids. Therefore, for the purposes of both quantum simulation and discovering new state of matter, it is desirable to introduce spin-orbit coupling into the field of ultracold quantum gases.
In 2011, Ian Spielman’s group in NIST first generated spin-orbit coupling in Bose gases . In that experiment, two counter-propagating laser beams are applied to the Bose condensate of Rubidium atoms. One of the two lasers is linearly polarized and the other is circularly polarized. Thus, when an atom absorbs a photon from one beam and then emits a photon to the other laser beam, their spin is flipped and also their momentum is also changed by the momentum difference of these two lasers. That is to say, the spin flip process is always accompanied by the change of momentum. In this way, the spin and their motion are locked together and a synthetic spin-orbit coupling is added into the motion of atoms. Such a coupling changes the single particle spectrum dramatically and the energy minimum is shifted from zero-momentum to finite momentum, which gives rise to unconventional condensate with intriguing phase or density patterns .
In our recent paper  we have for the first time applied the similar scheme to create spin-orbit coupling and demonstrate its effect in ultracold Fermi gases of Potassium-40. Fermi gas differs from Bose gas because fermions should obey Pauli exclusion principle, and therefore they have to occupy different momentum states and form a Fermi surface at low temperature. This also leads to the major difference for the manifestation of the spin-orbit coupling effects in a Fermi gas compared to in a Bose condensate. We have demonstrated several effects in our work.
Fig. 1: Spin oscillation under spin-orbit coupling. Different curves represent Fermi gases with different density.
First, if one starts with a fully polarized Fermi gas and applies a pulse of Raman coupling, the whole system will start Rabi oscillation. If all atoms oscillate with the same frequency, the Rabi oscillation will remain coherent for long time. However, in this system, atoms occupy different momenta and because of spin-orbit coupling, atoms with different momenta have different energies. Thus, different atoms oscillate with different periods, which leads to strong dephasing. This simulates spin-orbit coupling induced spin diffusion process of a spin polarized current in semiconductors. In our work, we also provide strong evidence for the topology change of Fermi surface. Using the momentum resolved radio-frequency spectroscopy, the single dispersion is also mapped out, where the effects of spin-orbit coupling is clearly demonstrated. Later on, MIT group led by Martin Zwierlein also studied spin-orbit coupled Fermi gas with lithium-6 atoms, and they measured spin-resolved single particle dispersion using spin-injection spectroscopy .
Fig 2: single particle dispersion measured by momentum resolved radio-frequency spectroscopy
In the near future, we plan to bring the system nearby a magnetic Feshbach resonance, and utilize the strong attraction there to create a fermion superfluid in the presence of spin-orbit coupling. Such a superfluid, when confined into one-dimensional geometry by optical lattices, becomes topological and displays Majorana edge mode, as discovered in nanowire recently . Realizing such a topological phase in cold atom setup will allow us to study its properties in a more controllable way.
To reach this goal, we also need to overcome several challenges. One major challenge is the heating due to spontaneous mission in the Raman process. For instance, for our experiment with Potassium-40, the temperature of the Fermi gases increases from around 0.2 of Fermi temperature to around 0.5 of Fermi temperature after Raman laser is turn on for around 100 ms. The heating is more profound for light atoms like Lithium. Such a problem may be overcome by further cooling fermions with very low temperature boson bath or by choosing other atoms like Yb or Dy, which have excited level with very narrow linewidth, and the spontaneous mission rate can be greatly suppressed.
The spin-orbit coupling generated in current experiment is a special type, which can be viewed as equal weight of Rashba and Dresselhaus. Another direction for future studies is to generate more complicated spin-orbit coupling, and one of the most interesting forms is pure Rashba because of the higher symmetry of this type of coupling. Such a coupling increases the single particle ground state degeneracy and the low-energy density-of-state, and thus it leads to many profound many-body quantum phenomena, as predicated by many of recent theoretical studies . It is exciting to discover them in experiments.
 Y. J. Lin, K. Jimenez-Garcia and I. B. Spielman, "Spin–orbit-coupled Bose–Einstein condensates", Nature, 471, 83 (2011). Abstract. 2Physics Article.
 Chunji Wang, Chao Gao, Chao-Ming Jian, and Hui Zhai, "Spin-Orbit Coupled Spinor Bose-Einstein Condensates", Physical Review Letters, 105, 160403 (2010). Abstract; Tin-Lun Ho and Shizhong Zhang, "Bose-Einstein Condensates with Spin-Orbit Interaction", Physical Review Letters, 107, 150403 (2011). Abstract.
 Pengjun Wang, Zeng-Qiang Yu, Zhengkun Fu, Jiao Miao, Lianghui Huang, Shijie Chai, Hui Zhai, and Jing Zhang, "Spin-Orbit Coupled Degenerate Fermi Gases", Physical Review Letters, 109, 095301 (2012). Abstract.
 Lawrence W. Cheuk, Ariel T. Sommer, Zoran Hadzibabic, Tarik Yefsah, Waseem S. Bakr, and Martin W. Zwierlein, "Spin-Injection Spectroscopy of a Spin-Orbit Coupled Fermi Gas", Physical Review Letters, 109, 095302 (2012). Abstract.
 V. Mourik, K. Zuo, S. M. Frolov, S. R. Plissard, E. P. A. M. Bakkers, and L. P. Kouwenhoven, "Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices", Science, 336, 1003 (2012). Abstract. 2Physics Article.
 For a review, see Hui Zhai, "Spin-orbit coupled quantum gases", International Journal of Modern Physics, 26, 1230001 (2012). Full Article.
Labels: Bose-Einstein Condensate 2