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The Josephson effect is a prominent phenomenon of quantum supercurrents that has been widely studied in superconductors and superfluids. Typical Josephson junctions consist of two realspace superconductors (superfluids) coupled through a weak tunneling barrier. Here we propose a momentum-space Josephson junction in a spin-orbit coupled Bose-Einstein condensate, where states with two different momenta are coupled through Raman-assisted tunneling. We show that Josephson currents can be induced not only by applying the equivalent of "voltages", but also by tuning tunneling phases. Such tunneling-phase-driven Josephson junctions in momentum space are characterized through both full mean field analysis and a concise two-level model, demonstrating the important role of interactions between atoms. Our scheme provides a platform for experimentally realizing momentum-space Josephson junctions and exploring their applications in quantummechanical circuits. arXiv:1710.06369v2 [cond-mat.quant-gas]

Double-well systems loaded with one, two, or many quantum particles give rise to intriguing dynamics, ranging from Josephson oscillation to self-trapping. This work presents theoretical and experimental results for two distinct double-well systems, both created using dilute rubidium Bose-Einstein condensates with particular emphasis placed on the role of interaction in the systems. The first is realized by creating an effective two-level system through Raman coupling of hyperfine states. The second is an effective two-level system in momentum space generated through the coupling by an optical lattice. Even though the non-interacting systems can, for a wide parameter range, be described by the same model Hamiltonian, the dynamics for these two realizations differ in the presence of interactions. The difference is attributed to scattering diagrams that contribute in the lattice coupled system but vanish in the Raman coupled system. The internal dynamics of the Bose-Einstein condensates for both coupling scenarios is probed through a Ramsey-type interference pulse sequence, which constitutes a key building block of atom interferometers. These results have important implications in a variety of contexts including lattice calibration experiments and momentum space lattices used for quantum analog simulations.

In the past few decades, the search for supersolid-like phases has attracted great attention in condensed matter and ultracold atom communities. Here we experimentally demonstrate a route for realizing a superfluid stripe-phase in a spin-orbit coupled Bose-Einstein condensate by employing a weak optical lattice to induce momentum-space hopping between two spin-orbit band minima. We characterize the striped ground state as a function of lattice coupling strength and spin-orbit detuning and find good agreement with mean-field simulations. We observe coherent Rabi oscillations in momentum space between two band minima and demonstrate a long lifetime of the ground state. Our work offers an exciting new and stable experimental platform for exploring superfluid stripe-phases and their exotic excitations, which may shed light on the properties of supersolid-like states.Introduction. Supersolids are an exotic phase of matter which simultaneously possess the crystalline properties of a solid and the unique flow properties of a superfluid [1]. Such simultaneous breaking of continuous translational symmetry and U(1) gauge symmetry was first predicted for solid helium [2,3], but convincing evidence of a supersolid state in this system has remained elusive [4]. In recent years, the experimental realization of spin-orbit coupling (SOC) in ultracold atomic gases [5][6][7][8][9][10][11][12][13][14][15][16][17] has opened a new pathway for demonstrating long-sought supersolidlike states [18][19][20][21][22][23][24][25][26][27][28][29][30].The lowest energy band in the SOC dispersion is characterized by two local minima at distinct momenta [5]. For a narrow range of system parameters, mean-field interactions within a Bose-Einstein condensate (BEC) favor a ground state which is composed of a coherent superposition of two plane-wave states at the dispersion minima [22]. This superposition leads to density modulations in real space, or stripes, therefore breaking translational symmetry while maintaining the superfluid phase correlation of a BEC. Such a stripe-phase was initially proposed for SOC BECs where the pseudospins are defined by two atomic hyperfine states [5]. While great experimental progress has been made in exploring the rich physics of such SOC systems, a ground state superfluid stripe-phase has not been observed in this context. The necessary parameter space is prohibitively sensitive to magnetic field fluctuations and the resulting density modulation is weak. However, recent works have attempted to sidestep these difficulties in creative ways, leading to experimental observations of some signatures of superfluid stripe phases in different systems [31][32][33][34].Despite these significant advances, the quest for a robust and long-lived platform for the experimental investigations of stripe-phase properties remains. In this Letter, we show that the superposition of two local band minima to form a supersolid-like ground state can be robustly achieved by means other than atomic interactions.Specifically, we engineer momen...

The intrinsic optical nonlinearities of linear structures, including conjugated chain polymers and nanowires, are shown to be dramatically enhanced by the judicious placement of a charge diverting path sufficiently short to create a large phase disruption in the dominant eigenfunctions along the main path of probability current. Phase disruption is proposed as a new general principle for the design of molecules, nanowires and any quasi-1D quantum system with large intrinsic response and does not require charge donor-acceptors at the ends. © The design and realization of ultrafast nonlinear optical materials with large responses to optical frequency electric fields remains an active field of pure and applied research [1][2][3][4]. To date, no general design rules for obtaining large nonlinearities from any structure have been articulated, and the response of materials remains well below that allowed by quantum physics. In this letter, we propose a general principle that may explain why modern molecules fall short of their potential and use it to demonstrate simple structures with nonlinear responses approaching the physical limits.The off-resonance electronic nonlinear optical response of a molecule is completely determined by its energy spectrum and transition moments. Normalized to its maximum value, the sum over states expression for the intrinsic first hyperpolarizability along the x-axis may be written as [5] where the sum is over all states, x nℓ is the n, ℓ element of the position matrix withx = x − x 00 , E n0 = E n − E 0 is the difference in energy of eigenstates n and 0, N is the number of electrons and m their mass. We include as many as 100 energy eigenstates to calculate β, but systems with large β are always well approximated using only three states. For brevity, we focus on the first hyperpolarizability, though our results also hold for the second hyperpolarizability, γ xxxx . For the remainder of this letter, all hyperpolarizabilities are divided by their maximum values and represent intrinsic tensor properties. It is evident from Eqn.(1) that a system optimized for nonlinear optics will necessarily have eigenfunctions with a large degree of overlap as well as a large change of dipole moment between contributing levels. This is an essential trade-off to achieve a large response. It is generally recognized that the hyperpolarizabilities of most molecules fall at least 30 times short of the limits. [5,6]. Monte Carlo simulations discovered the optimum energy spectrum for such molecules and provided a strong indicator of the origin of the gap [7]. Optimization of the effective potential energy an electron experiences across the main direction of a quasi-linear molecule showed that the hyperpolarizabilities may be increased by tuning a few parameters [8], by modulation of conjugation along a chain [9], or by donor-acceptor substitution and insertion of spacers [10]. However, there is no general rule about how to construct the ideal potential energy profile across a molecule to maximize the nonlinea...