Overcoming dispersive spreading of quantum wave packets via periodic nonlinear kicking

Abstract

We propose the suppression of dispersive spreading of wave packets governed by the free-space Schrödinger equation with a periodically pulsed nonlinear term. Using asymptotic analysis, we construct stroboscopically dispersionless quantum states that are physically reminiscent of, but mathematically different from, the well-known one-soliton solutions of the nonlinear Schrödinger equation with a constant (time-independent) nonlinearity. Our analytics are strongly supported by full numerical simulations. The predicted dispersionless wave packets can move with arbitrary velocity and can be realized in experiments involving ultracold atomic gases with temporally controlled interactions.

Quantum time mirrors for general two-band systems

“…This is identical to the magnetic field-free expression (30), with the Landau level energy E n substituting the k-mode energy E k of Eq. ( 26).…”

“…The non-linear protocol of Ref. [29] and generalizations [30] are designed for systems obeying a non-linear Schrödinger equation, such as atomic Bose-Einstein condensates in optical traps. The Quantum Time Mirror (QTM) of Ref.…”

Controlling Quantum Chaos: Optimal Coherent Targeting

“…Within the semiclassical propagation method called linearized wave packet dynamics [39,40] is an accounting for this spreading, and the method effectively constructs the corresponding unitary transformation in a configuration representation. The multidimensional expressions can be found in [22], and for an alternative approach for suppression of spreading through periodic nonlinear kicking see [41]. The main ingredients are the second derivatives of the generating function, S, which can be expressed in terms of the stability matrix elements (block ordering is consistent with the kicked rotor equations ahead) [40].…”

Non-dispersing wave packets in lattice Floquet systems

“…For example, non-linear Schödinger or Gross-Pitaevskii equations are known to host soliton solutions [6,7]. An alternative strategy is to invoke Floquet engineering [3,[8][9][10][11][12][13][14]. This was previously explored in the specific context of microwave-driven Rydberg atoms [3,10,15].…”