Cold atomic gases are perfect laboratories for realization of quantum simulators. In order to simulate solid state systems in the presence of magnetic fields special effort has to be made because atoms are charge neutral. There are different methods for realization of artificial magnetic fields, that is the creation of specific conditions so that the motion of neutral particles mimics the dynamics of charged particles in an effective magnetic field. Here, we consider adiabatic motion of atoms in the presence of an evanescent wave. Theoretical description of the adiabatic motion involves artificial vector and scalar potentials related to the Berry phases. Due to the large gradient of the evanescent field amplitude, the potentials can be strong enough to induce measurable effects in cold atomic gases. We show that the resulting artificial magnetic field is able to induce vortices in a Bose-Einstein condensate trapped close to a surface of a prism where the evanescent wave is created. We also analyze motion of an atomic cloud released from a magneto-optical trap that falls down on the surface of the prism. The artificial magnetic field is able to reflect falling atoms that can be observed experimentally.
Cold atomic gases are perfect laboratories for realization of quantum simulators. In order to simulate solid state systems in the presence of magnetic fields special effort has to be made because atoms are charge neutral. There are different methods for realization of artificial magnetic fields, that is the creation of specific conditions so that the motion of neutral particles mimics the dynamics of charged particles in an effective magnetic field. Here, we consider adiabatic motion of atoms in the presence of an evanescent wave. Theoretical description of the adiabatic motion involves artificial vector and scalar potentials related to the Berry phases. Due to the large gradient of the evanescent field amplitude, the potentials can be strong enough to induce measurable effects in cold atomic gases. We show that the resulting artificial magnetic field is able to induce vortices in a Bose-Einstein condensate trapped close to a surface of a prism where the evanescent wave is created. We also analyze motion of an atomic cloud released from a magneto-optical trap that falls down on the surface of the prism. The artificial magnetic field is able to reflect falling atoms that can be observed experimentally.
When a neutral atom moves in a properly designed laser field, its center-of-mass motion may mimic the dynamics of a charged particle in a magnetic field, with the emergence of a Lorentz-like force. In this Colloquium the physical principles at the basis of this artificial (synthetic) magnetism are presented. The corresponding Aharonov-Bohm phase is related to the Berry's phase that emerges when the atom adiabatically follows one of the dressed states of the atom-laser interaction. Some manifestations of artificial magnetism for a cold quantum gas, in particular, in terms of vortex nucleation are discussed. The analysis is then generalized to the simulation of non-Abelian gauge potentials and some striking consequences are presented, such as the emergence of an effective spin-orbit coupling. Both the cases of bulk gases and discrete systems, where atoms are trapped in an optical lattice, are addressed.
Ultracold gases are remarkably versatile and controllable systems with untapped potential to emulate a variety of quantum phenomena [1]. Atoms are, however, electrically neutral and therefore it is highly desirable to make them behave as charged particles. This capability has recently been demonstrated in a series of recent experiments [2–4]. Although many challenges remain ahead, atoms exposed to synthetic gauge field offer great opportunities for the realization of new classes of quantum materials with custom-designed properties, and with unforeseen applications. The first implementation of an effective magnetic field was accomplished by rotating an atomic cloud [5]. In the rotating frame of reference, an atom experiences the Coriolis force that emulates the Lorentz force experienced by a charged particle in a uniform magnetic field. Large vortex lattices have been created in this way, however, so far the strength of the effective magnetic field achieved by rotation is too weak to lead to new physics. An alternative approach invokes the vector potential, A, that induces a geometric phase as a charged particle moves around a closed loop. This notion of geometric phase can be adapted to a neutral atom that slowly moves in the presence of laser fields. If the lasers are chosen to ‘dress’ the internal atomic levels, so that the dressed eigenstates become position dependent, the center of mass adiabatically evolves according the operator p-A, instead of just p = −iℏ∇. The atom thus effectively moves as a charged particle in a magnetic field B = ∇ × A (see Fig. 1a). Exploiting this idea series of experiments have implemented artificial magnetic and electric fields [2–4]. The idea has also been implemented in the presence of a superimposed periodic optical lattice potential (see Fig. 1b). In this case, the length scale imposed by the lattice competes with the one associated with the magnetic field and can lead to frustration, manifested as an energy spectrum with fractal characteristics [2,3]. Light induced synthetic gauge fields: (a) A gas of neural atoms (green oval) can behave as a gas of charged particles when it is illuminated by a pair of laser beams (red arrows) that imparts momentum to the atoms and couples their internal (.|↑.〉, .|↓.〉) and motional degrees of freedom. The Raman beams that induce transitions between internal states also transfer two units of their linear momentum 2kL. This leads to the formation of dressed states (superpositions of states with different internal levels and center of mass momenta) which experience a modified kinetic energy, with an effective vector potential. If the effective vector potential has nonzero curl, the atoms move as charged particles in a magnetic field. (b) In the presence of an optical lattice potential, Raman beams can also induce an effective vector potential. In this case, the lattice is engineered so that along one direction atoms can tunnel between adjacent lattice sites (Jlight) only by absorbing and emitting photons from the beams. The imparted momentum from the lasers produces path-dependent phases that resemble the magnetic flux accumulated by a charged particle as it moves in a closed loop. The flux accumulated by the atoms when they move around a single unit cell, ϕ, can be significant (equivalent to the one generated by a real magnetic field of thousands tesla in an electronic system) and induce a fractal energy spectrum. Generalizations to emulate non-Abelian gauge potentials, associated in many cases to spin-orbit coupling can emerge when the geometric phase is replaced by a matrix acting on the internal Hilbert space [2–5]. This happens if there is a manifold of degenerate dressed states, such that even for arbitrarily slow motion, after traveling around a contour the particle ends up in a different internal state. Although various proposals for generating non-Abelian potentials exist, they remain to be implemented. On the other hand, Abelian spin-orbit coupling, arising from the momentum kicks imparted on the atom by the laser photons that drive internal transitions, has been realized in several laboratories using different laser configurations in alkali-metal (one outer electron) and alkaline-earth (two outer electrons) atoms [2–5]. There is a great vista ahead. For example, the inclusion of collisions or dipolar interactions will open a window to engineer fractional Hall liquids, unconventional superfluids and interacting topological phases. The creation of dynamical gauge fields important in many areas of physics such as quantum chromodynamics is also an open direction. The time is just ripe for investigating rich and unexplored physics with synthetic gauge fields for ultracold matter.
Artificial gauge fields are versatile tools that allow the dynamics of ultracold atoms in Bose-Einstein condensates to be influenced. Here we discuss a method of artificial gauge field generation stemming from the evanescent fields of the curved surface of an optical nanofiber. The exponential decay of the evanescent fields leads to large gradients in the generalized Rabi frequency and therefore to the presence of geometric vector and scalar potentials. By solving the Gross-Pitaevskii equation in the presence of the artificial gauge fields originating from the fundamental Hybrid mode (HE11) mode of the fiber, we show that vortex rings can be created in a controlled manner. We also calculate the magnetic fields resulting from the higher order HE21, Transverse electric mode (TE01), and Transverse magnetic mode (TM01) and compare them to the fundamental HE11 mode.
We propose a simple setup for introducing an artificial magnetic field for neutral atoms in 2D optical lattices. This setup is based on the phenomenon of photon-assistent tunneling and involves a low-frequency periodic driving of the optical lattice. We also address the problem of detecting this effective magnetic field. In particular, we discuss interference patterns of the atomic wave function and study the center of mass wave-packet dynamics, which shows some features of cyclotron dynamics of a classical charged particle. Introduction. – A major motivation of current research with cold atoms in optical lattices is the prospect of simulating the solid state physics. However, to have a full access to phenomena of the solid state physics this system (which can be considered as an artificial crystal) should be accomplished by artificial electric and magnetic fields. In present days experiments the former case of external electric field is routinely mimicked by accelerating the optical lattice [1–3], or by using the gravitational force [4–6] or a combination of gravitational and levitational forces [7]. The case of magnetic field is more difficult for laboratory realization because it requires a setup, where atomic wave function acquires a finite phase when the atom tunnels along a closed path on the lattice. This setup was suggested in the seminal paper [8], where the authors use two independent 2D optical lattices for two different internal atomic states, which are coupled by additional Raman lasers. The Rabi transition between internal states induces hopping of the atom between nearest lattice sites, where the required phase accumulation is achieved by using a special geometry for the Raman beams. This idea was developed further in Ref. [9, 10]. It was shown that one can also introduce an exotic (unphysical) field and non-Abelian gauge potentials by using the Raman-laser technique. For atoms in a harmonic trap (no lattice) the Raman scheme with 3 spin states of the F = 1 electronic ground state of Rb atom was realized in the recent experiment [11]. In this setup the magnitude of the effective magnetic field is defined by the gradient of the real magnetic field which splits the F = 1 level into Zeeman sublevels. In the paper the authors put forward a conjecture that this scheme should work in the presence of an optical lattice as well. We note that the cited experiment also illuminated a drawback of the Raman-laser based techniques. Namely, the spontaneous emission from the Raman beams removes atom from the trap, causing the population to decay within approx. 2 seconds.
In 1996, Lloyd [1] showed that the dynamics of complex many-body quantum systems can be efficiently simulated by quantum computers, an idea first put forward by Manin [2] and further developed by Feynman [3]. Although the first quantum computers of a few qubits have been realised experimentally [4, 5], the advent of scalable quantum computers might take another few decades. An alternative tool in the context of simulation is a highly controllable quantum system able to mimic the dynamics of other complex quantum systems, known as an analog quantum simulator. Cold neutral atoms and trapped ions have been shown to be versatile quantum simulators [6, 7] thanks to their high flexibility, controllability, and scalability. They permit one to study a wide range of problems arising from atomic physics, relativistic quantum physics, or cosmology [8]. Since neutral atoms do not carry any net charge, the simulation of electric and magnetic condensed matter phenomena, such as the spin Hall effect, seems out of reach. To overcome this apparent difficulty, the idea has been proposed to create artificial electromagnetic potentials for neutral atoms based on atom-light interaction [9– 12]. These artificial potentials act on neutral atoms as real electromagnetic potentials act on charged particles. Many works on artificial gauge potentials induced by atom-light interactions adopt a single-particle approach [12]. The predicted potentials are then supposed to be valid for a system of weakly interacting atoms. So far, the consequences of atom-atom interactions on the generation of artificial gauge fields has little been studied. The aim of this work is to study the artificial gauge fields arising from the interaction of two Rydberg atoms driven by a common laser field [13]. In this situation, we show that the combined atom-atom and atom-field interactions give rise to nonuniform, artificial gauge potentials. We identify the mechanism responsible for the emergence of these gauge potentials. Analytical expressions for the latter indicate that the strongest artificial magnetic fields are reached in the regime intermediate between the dipole blockade regime and the regime in which the atoms are sufficiently far apart such that atom-light interaction dominates over atom-atom interactions. We discuss the differences and similarities of artificial gauge fields originating from resonant dipole-dipole [14] and van der Waals [15] interactions. We also give an estimation of experimentally attainable artificial magnetic fields resulting from this mechanism and we discuss their detection through the deflection of the atomic motion. [1] S. Lloyd, Science 273, 1073 (1996). [2] Yu. I. Manin, Computable and uncomputable, Sovetskoye Radio, Moscow, 1980. [3] R. P. Feynman, Int. J. Theor. Phys. 21, 467 (1982). [4] L. DiCarlo, J. M. Chow, J. M. Gambetta, Lev S. Bishop, B. R. Johnson, D. I. Schuster, J. Majer, A. Blais, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, Nature 460, 240 (2009). [5] N. Xu, J. Zhu, D. Lu, X. Zhou, X. Peng, and J. Du, Phys. Rev. Lett. 108, 130501 (2012). [6] I. Buluta and F. Nori, Science 326, 108 (2009). [7] I. Bloch, J. Dalibard and S. Nascimbéne, Nature Physics 8, 267 (2012). [8] R. Blatt and C. F. Roos, Nature Physics 8, 277 (2012). [9] G. Juzeliunas and P. Öhberg, Phys. Rev. Lett. 93, 033602 (2004). [10] G. Juzeliunas, P. Öhberg, J. Ruseckas, and A. Klein, Phys. Rev. A 71, 053614 (2005). [11] G. Juzeliunas, J. Ruseckas, P. Öhberg, and M. Fleischhauer, Phys. Rev. A 73, 025602 (2006). [12] J. Dalibard, F. Gerbier, G. Juzeliu ̄nas, and P. Öhberg, Rev. Mod. Phys. 83, 1523 (2011). [13] A. Cesa and J. Martin, Phys. Rev. A 88,062703 (2013). [14] A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, Nature Physics 5, 115 (2009). [15] L. Béguin, A. Vernier, R. Chicireanu, T. Lahaye, and A. Browaeys, Phys. Rev. Lett. 110, 263201 (2013).
Quantum mechanically, static or applied gauge fields manifest themselves by directly coupling to a system's phase. Artificial gauge field techniques manipulate the phase of a Bose-Einstein condensate's order parameter, yielding effects present in condensed matter systems subject to magnetic fields, electric fields, or spin-orbit coupling. In this chapter, we explore the impact of these artificial gauge fields on Bose- Einstein condensates and explain the consequences. Several analogues to traditional condensed matter systems are enabled by these techniques, including the Hall effect, superfluid vortex nucleation in systems with artificial magnetic fields, and magnetic-like phase transitions in systems with spin-orbit coupling. Introduction Since the first experiments with Bose-Einstein condensates (BECs), researchers have exploited the universality of physical laws to draw analogies between the behavior of ultracold quantum gases and systems ranging from material to astrophysical. These analogous situations are deliberately engineered, giving cold-atom “quantum simulators” [1] that exhibit behavior either observed or predicted in analogous quantum systems. Superfluidity was one of the first many-body quantum phenomena demonstrated in BECs. For example, several experiments showed superfluid behavior by rapidly rotating the condensates and observing the formation of vortices [2, 3, 4, 5] – quantized point-defects in the BEC's order parameter. In the rotating frame of these experiments, this nucleation of vortices could be understood as the consequence of an artificial magnetic field [6] that arises via the formal equivalence of the rotating-frame Coriolis force and the Lorentz force, which we describe in Section 15.4.1. Together with other measurements, these results proved to be in excellent agreement with the predictions of the Gross-Pitaevskii equation (GPE) [7], a decades-old idealization of superfluid helium. Buoyed by the prospect for studying magnetic field–driven strongly correlated systems using these nearly ideal quantum gases, proposals for alternate techniques to simulate gauge fields were developed. These methods primarily employ an internal state–selective atom–light coupling, where the photon momentum provides the forces necessary to mimic a Lorentz force [8, 9, 10, 11, 12, 13, 14, 15, 16]. The first demonstration of this type of technique used a spatially dependent Ramantransition scheme to effect a magnetic field [17], and experiments demonstrating artificial electric fields [18] and spin-orbit coupling [19, 20, 21, 22, 23, 24] soon followed.