Stability of solitons in time-modulated two-dimensional lattices

We develop stability analysis for matter-wave solitons in a two-dimensional (2D) Bose-Einstein condensate loaded in an optical lattice (OL), to which periodic time modulation is applied, in different forms. The stability is studied by dint of the variational approximation and systematic simulations. For solitons in the semi-infinite gap, well-defined stability patterns are produced under the action of the attractive nonlinearity, clearly exhibiting the presence of resonance frequencies. The analysis is reported for several time-modulation formats, including the case of in-phase modulations of both quasi-1D sublattices, which build the 2D square-shaped OL, and setups with asynchronous modulation of the sublattices. In particular, when the modulations of two sublattices are phase-shifted by {\delta}={\pi}/2, the stability map is not improved, as the originally well-structured stability pattern becomes fuzzy and the stability at high modulation frequencies is considerably reduced. Mixed results are obtained for anti-phase modulations of the sublattices ({\delta}={\pi}), where extended stability regions are found for low modulation frequencies, but for high frequencies the stability is weakened. The analysis is also performed in the case of the repulsive nonlinearity, for solitons in the first finite bandgap. It is concluded that, even though stability regions may be found, distinct stability boundaries for the gap solitons cannot be identified clearly. Finally, the stability is also explored for vortex solitons of both the "square-shaped" and "rhombic" types (i.e., off- and on-site-centered ones).Comment: Nonlinear Dynamics, to be publishe

New constraints on light vectors coupled to anomalous currents

We derive new constraints on light vectors coupled to Standard Model (SM) fermions, when the corresponding SM current is broken by the chiral anomaly. Cancellation of the anomaly by heavy fermions results, in the low-energy theory, in Wess-Zumino type interactions between the new vector and the SM gauge bosons. These interactions are determined by the requirement that the heavy sector preserves the SM gauge groups, and lead to (energy / vector mass)^2 enhanced rates for processes involving the longitudinal mode of the new vector. Taking the example of a vector coupled to baryon number, Z decays and flavour changing neutral current meson decays via the new vector can occur with (weak scale / vector mass)^2 enhanced rates. These processes place significantly stronger coupling bounds than others considered in the literature, over a wide range of vector masses.Comment: 6 pages, 1 figure; v2: corrected small numerical errors in Fig.

Parametric Resonance Production of Ultralight Vector Dark Matter

Vector bosons heavier than $10^{-22}$ eV can be viable dark matter candidates with distinctive experimental signatures. Ultralight dark matter generally requires a non-thermal origin to achieve the observed density, while still behaving like a pressureless fluid at late times. We show that such a production mechanism naturally occurs for vectors whose mass originates from a dark Higgs. If the dark Higgs has a large field value after inflation, the energy in the Higgs field can be efficiently transferred to vectors through parametric resonance. Computing the resulting abundance and spectra requires careful treatment of the transverse and longitudinal components, whose dynamics are governed by distinct differential equations. We study these equations in detail and find that the mass of the vector may be as low as $10 ^{ - 18 }$ eV, while making up the dominant dark matter abundance. This opens up a wide mass range of vector dark matter as cosmologically viable, further motivating their experimental search.Comment: discussion clarified, matches publication in PR

Light vectors coupled to bosonic currents

New spin-1 particles with masses below the weak scale are present in many theories of beyond Standard Model (SM) physics. In this work, we extend previous analyses by systematically considering the couplings of such a vector to the bosonic sector of the SM, focusing on models that lead to mass-mixing with the Z boson. These couplings generically lead to enhanced emission of the vector's longitudinal mode, both in Higgs decays and in flavor changing meson decays. We present bounds in the SM+X effective theory and investigate their model-dependence. For the case of Higgs decays, we point out that tree-level vector emission is, depending on the model, not always enhanced, affecting the constraints. For meson decays, which are the dominant constraints at small vector masses, we find that while $B$ decay constraints can be weakened by fine-tuning UV parameters, it is generically difficult to suppress the stringent constraints from kaon decays.Comment: 11 pages, 5 figure

Spontaneous symmetry breaking in a split potential box

We report results of the analysis of the spontaneous symmetry breaking (SSB) in the basic (actually, simplest) model which is capable to produce the SSB phenomenology in the one-dimensional setting. It is based on the Gross-Pitaevskii - nonlinear Schroedinger equation with the cubic self-attractive term and a double-well-potential built as an infinitely deep potential box split by a narrow (delta-functional) barrier. The barrier's strength, epsilon, is the single free parameter of the scaled form of the model. It may be implemented in atomic Bose-Einstein condensates and nonlinear optics. The SSB bifurcation of the symmetric ground state (GS) is predicted analytically in two limit cases, viz., for deep or weak splitting of the potential box by the barrier. For the generic case, a variational approximation (VA) is elaborated. The analytical findings are presented along with systematic numerical results. Stability of stationary states is studied through the calculation of eigenvalues for small perturbations, and by means of direct simulations. The GS always undergoes the SSB bifurcation of the supercritical type, as predicted by the VA at moderate values of epsilon, although the VA fails at small epsilon, due to inapplicability of the underlying ansatz in that case. However, the latter case is correctly treated by the approximation based on a soliton ansatz. On top of the GS, the first and second excited states are studied too. The antisymmetric mode (the first excited state) is destabilized at a critical value of its norm. The second excited state undergoes the SSB bifurcation, like the GS, but, unlike it, the bifurcation produces an unstable asymmetric mode. All unstable modes tend to spontaneously reshape into the asymmetric GS.Comment: Physical Review E, in pres

Direct Detection Signals from Absorption of Fermionic Dark Matter

We present a new class of direct detection signals; absorption of fermionic dark matter. We enumerate the operators through dimension six which lead to fermionic absorption, study their direct detection prospects, and summarize additional constraints on their suppression scale. Such dark matter is inherently unstable as there is no symmetry which prevents dark matter decays. Nevertheless, we show that fermionic dark matter absorption can be observed in direct detection and neutrino experiments while ensuring consistency with the observed dark matter abundance and required lifetime. For dark matter masses well below the GeV scale, dedicated searches for these signals at current and future experiments can probe orders of magnitude of unexplored parameter space.Comment: 7 pages, 2 figures. v2: published in PRL with minor revisions and changes to Fig 2 (no change to results

Dark forces coupled to non-conserved currents

New light vectors with dimension-4 couplings to Standard Model states have (energy / vector mass)^2 enhanced production rates unless the current they couple to is conserved. These processes allow us to derive new constraints on the couplings of such vectors, that are significantly stronger than the previous literature for a wide variety of models. Examples include vectors with axial couplings to quarks and vectors coupled to currents (such as baryon number) that are only broken by the chiral anomaly. Our new limits arise from a range of processes, including rare Z decays and flavor changing meson decays, and rule out a number of phenomenologically-motivated proposals.Comment: 20 pages, 3 figures; v2: fixed small numerical errors in Fig 1 and Fig

Holding spatial solitons in a pumped cavity with the help of nonlinear potentials

We introduce a one-dimensional model of a cavity with the Kerr nonlinearity and saturated gain, designed so as to keep solitons in the state of shuttle motion. The solitons are always unstable in the cavity bounded by the usual potential barriers, due to accumulation of noise generated by the linear gain. Complete stabilization of the shuttling soliton is achieved if the linear barrier potentials are replaced by nonlinear ones, which trap the soliton, being transparent to the radiation. The removal of the noise from the cavity is additionally facilitated by an external ramp potential. The stable dynamical regimes are found numerically, and their basic properties are explained analytically.Comment: Optics Letters, to be publishe

Running Measurement Protocol for the Quantum First-detection problem

The problem of the detection statistics of a quantum walker has received increasing interest, connected as it is to the problem of quantum search. We investigate the effect of employing a moving detector, using a projective measurement approach with fixed sampling time $\tau$, with the detector moving right before every detection attempt. For a tight-binding quantum walk on the line, the moving detector allows one to target a specific range of group velocities of the walker, qualitatively modifying the behavior of the quantum first-detection probabilities. We map the problem to that of a stationary detector with a modified unitary evolution operator and use established methods for the solution of that problem to study the first-detection statistics for a moving detector on a finite ring and on an infinite 1D lattice. On the line, the system exhibits a dynamical phase transition at a critical value of $\tau$, from a state where detection decreases exponentially in time and the total detection is very small, to a state with power-law decay and a significantly higher probability to detect the particle. The exponent describing the power-law decay of the detection probability at this critical $\tau$ is 10/3, as opposed to 3 for every larger $\tau$. In addition, the moving detector strongly modifies the Zeno effect

Spontaneous symmetry breaking of self-trapped and leaky modes in quasi-double-well potentials

We investigate competition between two phase transitions of the second kind induced by the self-attractive nonlinearity, viz., self-trapping of the leaky modes, and spontaneous symmetry breaking (SSB) of both fully trapped and leaky states. We use a one-dimensional mean-field model, which combines the cubic nonlinearity and a double-well-potential (DWP) structure with an elevated floor, which supports leaky modes (quasi-bound states) in the linear limit. The setting can be implemented in nonlinear optics and BEC. The order in which the SSB and self-trapping transitions take place with the growth of the nonlinearity strength depends on the height of the central barrier of the DWP: the SSB happens first if the barrier is relatively high, while self-trapping comes first if the barrier is lower. The SSB of the leaky modes is characterized by specific asymmetry of their radiation tails, which, in addition, feature a resonant dependence on the relation between the total size of the system and radiation wavelength. As a result of the SSB, the instability of symmetric modes initiates spontaneous Josephson oscillations. Collisions of freely moving solitons with the DWP structure admit trapping of an incident soliton into a state of persistent shuttle motion, due to emission of radiation. The study is carried out numerically, and basic results are explained by means of analytical considerations.Comment: Physical Review A, in pres