Nonadiabaticity and large fluctuations in a many-particle Landau-Zener problem

Abstract

We consider the behavior of an interacting many particle system under slow external driving -a many body generalization of the Landau-Zener paradigm. We find that a conspiracy of interactions and driving leads to physics profoundly different from that of the single particle limit: for practically all values of the driving rate the particle distributions in Hilbert space are very broad, a phenomenon caused by a strong amplification of quantum fluctuations in the driving process. These fluctuations are 'non-adiabatic' in that even at very slow driving it is exceedingly difficult to push the center of the distribution towards the limit of full ground state occupancy. We obtain these results by a number of complementary theoretical approaches, including diagrammatic perturbation theory, semiclassical analysis, and exact diagonalization.

Nonequilibrium quantum phase transitions in the Ising model

“…and H k is the FBdG Hamiltonian equation (8). figure 3 depicts the dynamics of the magnetization density in the thermodynamic limit calculated using RWA (black curve).…”

“…as defined in equation (8). The quasienergy gap in the fermion picture is given by ∆E k,m = ε (+) k,m −ε (−) k,m = 2ε k,m .…”

“…Recently, experimental realizations of one-dimensional spin chains have been suggested, where a quantum simulation of the system close to the phase transition is possible, and a wide freedom on the control of the parameters is achieved [2][3][4][5][6][7]. The quantum control of many-body systems by a driving field has attracted considerable interest, both theoretical and experimental, with workers from very different communities beginning to look at driven models [8][9][10][11][12][13][14][15][16][17]. The possibility of manipulating the quantum state of a system by means of a classical external control allows one to explore novel states of matter and effective interactions which are absent in equilibrium [16][17][18][19].…”

Adiabatic State Preparation of Interacting Two-Level Systems

“…Provided the gap induced by the applied field is large compared with the sweep rate the process is adiabatic, and the wavefunction is transferred from the initial ground state to the target state with high probability. The presence of an external field creating a gap contrasts with some recent analyses of many-body Landau-Zener problems [4][5][6][7][8] in which there is no external field creating a gap and non-adiabatic effects appear.ARP is a well-established technique in nuclear magnetic resonance, where chirped radio frequency pulses are used to manipulate nuclear spins [9]. More recently, there have been a number of investigations into using ARP with optical pulses to control excitons in quantum dots [1,[10][11][12], including the creation of entangled states [13][14][15][16].…”

Dynamically generated reduction of the mean photon number in the Dicke model

“…Thus the system is supposed to be in the ground state |ψ 0 of the time-independent Dicke HamiltonianĤ D for t < 0 and to evolve according to the time-dependent Dicke HamiltonianĤ RD (t) for t > 0. In the rotated frame we have to solve the Schrödinger equation, (15), for |ψ ROT (t) with the initial condition |ψ ROT (0) = |ψ 0 . We have used both the numerical technique for the full quantum problem (explained in Sec.…”