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The Bose–Einstein condensates (BECs) are seen during the studies in atomic optics, cavity opto-mechanics, cavity quantum electrodynamics, black-hole astrophysics, laser optics and atomtronics. Under investigation in this paper is a (2+1)-dimensional Gross–Pitaevskii equation with time-varying trapping potential which describes the dynamics of a (2+1)-dimensional BEC. Based on the Kadomtsev–Petviashvili hierarchy reduction, we construct the bilinear forms and the N th order rogue-wave solutions in terms of the Gramian. With the help of the analytic and graphic analysis, we exhibit the first- and second-order rogue waves under the influence of the strength of the interatomic interaction, α ( t ) , and of Ω ( t ) = ω R ∕ ω Z , where t is the scaled time, ω R and ω Z are the confinement frequencies in the radial and axial directions: When Ω ( t ) = 0 , the first-order rogue wave exhibits as an eye-shaped distribution; When Ω ( t ) is a periodic function, the rogue wave periodically raises; When Ω ( t ) is an exponential function, the rogue wave appears on the exponentially increasing background; When α ( t ) decreases, background and amplitude of the rogue wave both increase. The second-order rogue waves reach the maxima only once or three times when Ω ( t ) is a constant. With Ω ( t ) being the exponential function, the backgrounds of the second-order rogue waves exponentially increase with t increasing.

We study the effects of dissipation or gain on Josephson dynamics of superfluid Fermi gases in a double-well potential. To this end, we phenomenologically introduce an imaginary term into the order-parameter equation, and derive a nonconservative and full two-mode (fTM) model under the two-mode approximation. The fTM model contains cross (high-order) interactions relevant to mixed products of wavefunctions at different sites, which are ignored by the two-mode (TM) model. It is because the cross interactions that the time-dependent equation for the total number of atoms is coupled to population imbalance and relative phase. Therefore, the derived nonconservative fTM model can lead to new Josephson behaviors that cannot be captured within the TM model. Specially, we find that the transitions of Josephson oscillations between the zero-phase and π-phase modes can be controlled by dissipation or gain, which may have applications in atomtronics devices serving as a switch or gate.

We present a mechanism for quantum gates where the qubits are encoded in the population distribution of two component ultracold atoms trapped in a species-selective triple-well potential. The gate operation is a specific application of a new design for an atomtronics transistor where inter-species interaction is used to control transport, and can be realized with either individual atoms or aggregates like Bose-Einstein condensates (BEC). We demonstrate the operational principle with a static external potential, and show feasible implementation with a smooth dynamical potential., 5 pages,5 figures

Optical Feshbach resonance can induce spatially varying interactions in ultra-cold atoms. Its applications to pancake-shaped clouds of bosons and fermions enable one to study several fresh phenomena. We examine possibilities of unexplored structures such as a bosonic superfluid enclave inside a Mott insulator and a normal-gas core enclosed by a fermionic superfluid shell. We discuss feasible experimental setups and signatures of those interesting structures. While a superfluid enclave in a Mott insulator may be useful for atomic devices in atomtronics, the superconducting islands observed in scanning–tunneling microscopy of heavily underdoped high-temperature superconductors may be simulated by ultra-cold fermions.

With the announcement of t he recent successful production of a Bose-Einstein condensate (BEC) of photons, a circle has been completed which started in 1925 with the vision of Albert Einstein and Satyendra Nath Bose – a sustained macroscopic condensed state of matter where all atoms are in the same lowest quantum state. The creation of an all-optical BEC, involving a surprisingly straightforward “tabletop” method which bypasses the normally requisite laser/evaporative cooling equipment and ultra-high vacuum chambers necessary for production of the standard delicate atomic BEC, elevates this phenomenon to a new level well beyond its current perception as mere laboratory curiosity. Accordingly, this development certainly heralds eventual incorporation of atomic and photon BECs as standard operating components of energy-efficient mechanical, optical and electrical systems, implying novel ingenious engineering protocols amenable to all the tools of non-linear and quantum optics. Pointing towards such a promising technological future are the suggestion that a photon BEC could serve as a new high-energy ultra-violet (UV) laser photon source, as well as the recent unprecedented implementation of a closed-loop atom circuit (toroidal atomic BEC) demonstrating precise control of superfluid current flow, forecasting the coveted development of an atomic SQUID. Perhaps more significantly, the new highly robust and manageable optical BEC will allow heretofore unfathomable precise probing of the atomic and nano-levels of nature, affording novel high-quality testing procedures of the major foundations of quantum mechanics itself. Such a primary advancement, providing a clearer glimpse into the microscopic realms, may present us as never before with an unprecedented view of the quantum engine that underpins physical reality itself and help place the contextual nature of entanglement and quantum superposition on a firmer foundation. Thus, further progress in achieving mastery over the precise flexible manipulation of BEC states could demonstrate that quantum contextuality might be an unsuspected over-arching archetypal principle in nature, leading to new insight in regards to the interpretation of quantum mechanics as applied to all levels of nature. Moreover, it will be shown that this concealed and hence heretofore unsuspected contextual aspect of natural laws, as exemplified by the dynamics underlying BEC structure, could be brought to bear to account for physical anomalies inexplicable using current paradigms, such as the claimed energy yields from low-energy nuclear reactions (as represented by the so-called process of “cold fusion”), making this phenomenon more tractable and rendered less controversial.