Experimental observation of Zitterbewegung is considered a holy grail of the modern physics since its debut in 1930 by Schrdinger. In this thesis we describe the first experimental observation of this effect in a two-dimensional ultracold atomic wave packet. In addition to that, we have also revealed the anisotropic of nature of Zitterbewegung, in the presence of non-Abelian Gauge field.
Experimental observation of Zitterbewegung is considered a holy grail of the modern physics since its debut in 1930 by Schrdinger. In this thesis we describe the first experimental observation of this effect in a two-dimensional ultracold atomic wave packet. In addition to that, we have also revealed the anisotropic of nature of Zitterbewegung, in the presence of non-Abelian Gauge field.
It is generally admitted that in quantum mechanics, the electromagnetic potentials have physical interpretations otherwise absent in classical physics as illustrated by the Aharonov-Bohm effect. In 1984, Berry interpreted this effect as a geometrical phase factor. The same year, Wilczek and Zee generalized the concept of Berry phases to degenerate levels and showed that a non-Abelian gauge field arises in these systems. In sharp contrast with the Abelian case, spatially uniform non-Abelian gauge fields can induce particle noninertial motion. We explore this intriguing phenomenon with a degenerated Fermionic atomic gas subject to a two-dimensional synthetic SU(2) non-Abelian gauge field. We reveal the spin Hall nature of the noninertial dynamic as well as its anisotropy in amplitude and frequency due to the spin texture of the system. We finally draw the similarities and differences of the observed wave packet dynamic and the celebrated Zitterbewegung effect of the relativistic Dirac equation.
Gauge fields play a prominent role in modern physics from electromagnetic theory to standard model of particle physics. These are cutting edge mathematical tools to understand fundamental forces and interaction between sub-atomic particles. Though gauge fields are considered natural tools of study in high-energy physics, they can be extended to low-energy condensed matter physics to study the behaviour of quantum particles in special environments like electrons in a magnetic field. Apart from naturally occurring gauge fields, controllable artificial gauge fields can be used to tailor physical effects on quantum systems like neutral atoms, qubits, photons, anions etc. This thesis reports the study of laser-induced artificial non-Abelian gauge fields interacting with an ultracold atomic wave packet in free space. In sharp contrast to the Abelian gauge fields, spatially uniform non-Abelian gauge fields can induce non-inertial motion of a particle. This motion is locked to the pseudo-spin state of the system and induces spin-orbit coupling. These non-Abelian gauge fields are experimentally realized by adiabatic evolution of the state of the atoms in the degenerate subspace of the coupling Hamiltonians. We produce SU(2) and SU(3) non-Abelian gauge fields using doubly degenerate dark state subspace of tripod and triply degenerate dark state subspace of double-tripod atom-light coupling schemes, respectively. Using the SU(2) gauge field in one dimension, we demonstrate the function of an atomtronic Datta-Das transistor (DDT) where spin polarized atoms enter the gate region and exit with their spin orientation controlled by the gate parameter analogous to the gate voltage in conventional field effect transistor. We demonstrate the geometric nature of the spin rotation in our DDT by showing insensitivity of the result to the input velocity and velocity dispersion of the atomic cloud. We have also implemented a Ramsey interferometric sequence to extract the phase of the output state of the DDT showing that the spin rotation by the DDT is coherent. In two dimensions, the dynamics of the wave packet in SU(2) gauge field show Zitterbewegung oscillations revealing spin Hall effect characteristics of the system. Whereas the dynamics of the wave packet in SU(3) gauge field show oscillations with multiple frequencies emulating color-orbit coupling. These frequencies correspond to the energy separation between the eigenstates of the Hamiltonian. Using the SU(3) Hamiltonian, we show two paths of reaching the same final state from the initial state demonstrating the existence of additional ladder operators in the SU(3) system in addition to the well-known raising and lowering operators of angular momentum represented by SU(2) symmetry. With this study, we realize a system that can be used to study the rich physics of SU(3) Hamiltonians on table top experiments.
Non-Abelian gauge field plays an important role in high-energy physics through Yang-Mill theory, in condensed-matter physics, for instance, with anomalous quantum Hall effect, and in quantum information. In its SU(2) symmetry version, Hamiltonians with non-Abelian gauge field reduce to spin-orbit coupling-like systems, taking the general form: H = p 2 /2m+ A.p /m , where m is the mass of the particle, p the momentum and A the non-Abelian gauge field with 2x2 matrix components, decomposed on SU(2) Lie group generators. These class of Hamiltonians can be simulate with ultracold gas [1] using various methods [2] . The topological properties of spin-orbit-coupled system have been explore analysing the energy bands in 2D Fermionic system [3] . Here, the eigenenergies have momentum dependence, leading to Rabi flopping with periodic change of quasi-momentum, even if the non-Abelian gauge field is homogenous. This oscillation is similar to relativistic Zitterbewegung predicted in Dirac equation and simulated in ultracold system [4] .
The dynamics of ultracold neutral atoms subject to a non-Abelian gauge field is investigated. In particular we analyze in detail a simple experimental scheme to achieve a con- stant, but non-Abelian gauge field, and discuss in the frame of this gauge field the non-Abelian Aharanov-Bohm effect. In the last part of this paper, we discuss intrinsic non-Abelian effects in the dynamics of cold atomic wavepackets. the implementation of these proposals, ultracold atoms would offer a unique testbed for the analysis of non-trivial non- Abelian effects on the quantum dynamics of multicomponent wavepackets. In this paper, we investigate the wave packet dynam- ics of a cloud of ultracold atoms in the presence of a non- Abelian gauge potential. In Sect. 2 we discuss how this un- doubtedly rather exotic scenario can be envisaged in a sam- ple of cold atoms where the internal electronic energy levels are addressed by laser fields with a nontrivial spatial phase and intensity distribution. This setup opens up a number of new scenarios for ultracold gases, allowing for the study of non-Abelian atom optics, which naturally ties together opti- cal and magnetic effects. Remarkably, as shown in Sect. 2, even very simple laser arrangements may induce non-trivial cold-atom dynamics. As a first example of this non-trivial dynamics, we discuss in Sect. 3 a possible optical tweezer experiment including a non-Abelian flux, for which the pop- ulation transfer between internal states crucially depends on the path taken (non-Abelian Aharonov-Bohm effect). This effect resembles indeed what one would expect from scat- tering protons onto a non-Abelian flux line where the proton can be transferred into a neutron (8). The tweezer experiment discussed in Sect. 3 just involves the internal-state dynamics, without exploring the rich dynamics resulting from the in- terplay between external and internal degrees of freedom in non-Abelian gauge fields. Section 4 is devoted to the analy- sis of this interplay. In particular, we show that the dynamics of cold-atom wavepackets can be significantly affected by in- trinsically non-Abelian effects, which are crucially dependent on the initial momentum distribution of the wavepacket. We consider in particular the relevant examples of wavepacket propagation and wavepacket reflection at an atomic mirror. Finally, we conclude in Sect. 5.
We propose an optical lattice scheme which would permit the experimental observation of Zitterbewegung (ZB) with ultracold, neutral atoms. A four-level tripod variant of the setup for stimulated Raman adiabatic passage (STIRAP) has previously been proposed for generating non-Abelian gauge fields. Dirac-like Hamiltonians, which exhibit ZB, are simple examples of such non-Abelian gauge fields; we show how a variety of them can arise, and how ZB can be observed, in a tripod system. We predict that the ZB should occur at experimentally accessible frequencies and amplitudes.
Ultracold atoms which are subject to ultra-relativistic dynamics are investigated. By using optically induced gauge potentials we show that the dynamics of the atoms is governed by a Dirac-type equation. To illustrate this we study the trembling motion of the centre of mass for an effective two-level system, historically called Zitterbewegung. Its origin is described in detail, where in particular the role of the finite width of the atomic wave packets is seen to induce a damping of both the centre of mass dynamics and the dynamics of the populations of the two levels.