Spin-orbit coupled Bose-Einstein condensates in a double well

We study the quantum dynamics of a spin-orbit (SO) coupled Bose-Einstein condensate (BEC) in a double-well potential inspired by the experimental protocol recently developed by NIST group. We focus on the regime where the number of atoms is very large and perform a two-mode approximation. An analytical solution of the two-site Bose-Hubbard-like Hamiltonian is found for several limiting cases, which range from a strong Raman coupling to a strong Josephson coupling, ending with the complete model in the presence of weak nonlinear interactions. Depending on the particular limit, different approaches are chosen: a mapping onto an SU(2) spin problem together with a Holstein-Primakoff transformation in the first two cases and a rotating wave approximation (RWA) when dealing with the complete model. The quantum evolution of the number difference of bosons with equal or different spin between the two wells is investigated in a wide range of parameters; finally the corresponding total atomic current and the spin current are computed. We show a spin Josephson effect which could be detected in experiments and employed to build up realistic devices.Comment: 18 page

Nonequilibrium properties of an atomic quantum dot coupled to a Bose-Einstein condensate

We study nonequilibrium properties of an atomic quantum dot (AQD) coupled to a Bose-Einstein condensate (BEC) within Keldysh-Green's function formalism when the AQD level is varied harmonically in time. Nonequilibrium features in the AQD energy absorption spectrum are the side peaks that develop as an effect of photon absorption and emission. We show that atoms can be efficiently transferred from the BEC into the AQD for the parameter regime of current experiments with cold atoms.Comment: 8 pages, 2 figures, to appear in the special issue "Novel Quantum Phases and Mesoscopic Physics in Quantum Gases" of The European Physical Journal - Special Topic

Transport properties in bilayer Quantum Hall systems in the presence of a topological defect

Following a suggestion given in Phys. Lett. B 571(2003) 621, we show how a bilayer Quantum Hall system at fillings nu =1/p+1 can exhibit a point-like topological defect in its edge state structure. Indeed our CFT theory for such a system, the Twisted Model (TM), gives rise in a natural way to such a feature in the twisted sector. Our results are in agreement with recent experimental findings (Phys. Rev. B 72 (2005) 041305) which evidence the presence of a topological defect in the transport properties of the bilayer system.Comment: 10 pages, 4 figures; talk given by A. Naddeo at "X Training Course in the Physics of Correlated Electron Systems and High-Tc Superconductors, Vietri sul Mare (SA),Italy, 3-14 October 200

Introducing the basic concepts of general relativity in high schools

INTRODUCTION Unlike the case of quantum mechanics, the teaching at the high school level of general relativity (GR) has been the target of relatively minor efforts by researchers in physics education (Kersting, Henriksen, Boe & Angell 2018), despite both subjects being included in the curricula in many countries. Although its foundations are not as controversial as those of quantum mechanics, GR also rests on some subtle conceptual steps, and, moreover, it cannot be probed using real experiments. Hence, teaching it at the high school level presents important challenges. However, the conceptual steps needed for GR are firmly founded in classical mechanics, electromagnetism, and special relativity (Sciama 1969), and when suitably presented and supported by adequate material, they can be within grasp of final year pupils. In this presentation, we outline and discuss a proposal in which these basic concepts are gradually introduced as natural extensions of those that physics pupils know, in a simple yet nontrivial way, which goes beyond the current textbook approaches. The latter, indeed, usually present little more than a popular level account. Typically, they rely on the famous elastic sheet analogy, which in turn is based on the iconic fact that GR geometrizes the gravitational field. However, such a statement takes quite a long route to be established, hence without adequate motivation, usually results in students getting the impression that the theory comes out of the blue. Also, the analogy is not very accurate, failing to highlight the role of time in the theory. FROM CLASSICAL MECHANICS TO GR: A PROPOSAL Our proposal starts from a critical rethinking of the principles of Newtonian mechanics, focusing on the role of inertia and of inertial forces, and on the principle of equivalence of gravitational and inertial mass. This part can be supplemented by real experiments and simulations. The next step involves special relativity, discussing the apparently unrelated problems of extending the relativity principle to non-inertial frames, and of reconciling gravity with the universal speed limit. Then, the way in which the equivalence principle allows to extend the special relativity principle is discussed with the help of Einstein’s elevator thought experiment. Crucial here is the discussion of how the equivalence principle is elevated from mechanics to all physical phenomena and how it is reconciled with the fact that special relativity teaches us that inertial mass is a form of energy. By means of some thought experiments, in fact, it is possible to quantitatively show that the same is true for the gravitational mass (Einstein, 1911). Then, by further thought experiments and simple calculations, some consequences of this principle can be explored: the gravitational redshift and time-dilation, the application to the Global Positioning System, and the gravitational bending of light. At this point, students should be invited to reflect on the special features that a theory based on special relativity and on Einstein’s equivalence principle should have, in comparison with electromagnetism, and the consequences should be explored. Finally, the thought experiment of the rotating disc (Janssen, 2014) can provide a way of motivating the well-known geometric picture. REFERENCES Einstein A. (1911). Einfluss der Schwerkraft auf die Ausbreitung des Lichtes. Ann. Phys. (Ser.4), 35, 898. Janssen M. (2014). “No success like failure…”. Einstein’s quest for general relativity, 1907-1920. In M.Janssen & C. Lehner (Eds.), The Cambridge companion to Einstein (pp. 167-227). Cambridge: Cambridge University Press. Kersting, M., Henriksen, E. K., Boe, M.V., & Angell. C. (2018). General relativity in upper secondary school: Design and evaluation of an online environment using the model of educational reconstruction. Phys. Rev. Phys. Educ. Res. 14, 010130. Sciama, D. (1969). The physical foundations of general relativity, New. York: Doubleday

Quantum dynamics of a binary mixture of BECs in a double well potential: an Holstein-Primakoff approach

We study the quantum dynamics of a binary mixture of Bose-Einstein condensates (BEC) in a double-well potential starting from a two-mode Bose-Hubbard Hamiltonian. Focussing on the regime where the number of atoms is very large, a mapping onto a SU(2) spin problem together with a Holstein-Primakoff transformation is performed. The quantum evolution of the number difference of bosons between the two wells is investigated for different initial conditions, which range from the case of a small imbalance between the two wells to a coherent spin state. The results show an instability towards a phase-separation above a critical positive value of the interspecies interaction while the system evolves towards a coherent tunneling regime for negative interspecies interactions. A comparison with a semiclassical approach is discussed together with some implications on the experimental realization of phase separation with cold atoms.Comment: 12 pages, 7 figures, accepted for publication in J. Phys.

Quantum Bose Josephson Junction with binary mixtures of BECs

We study the quantum behaviour of a binary mixture of Bose-Einstein condensates (BEC) in a double-well potential starting from a two-mode Bose-Hubbard Hamiltonian. We focus on the small tunneling amplitude regime and apply perturbation theory up to second order. Analytical expressions for the energy eigenvalues and eigenstates are obtained. Then the quantum evolution of the number difference of bosons between the two potential wells is fully investigated for two different initial conditions: completely localized states and coherent spin states. In the first case both the short and the long time dynamics is studied and a rich behaviour is found, ranging from small amplitude oscillations and collapses and revivals to coherent tunneling. In the second case the short-time scale evolution of number difference is determined and a more irregular dynamics is evidenced. Finally, the formation of Schroedinger cat states is considered and shown to affect the momentum distribution.Comment: 14 pages, 4 figure