Single-shot simulations of dynamic quantum many-body systems

Abstract

Single experimental shots of ultracold quantum gases sample the many-particle probability distribution. In a few cases such single shots could be successfully simulated from a given many-body wavefunction 1-4 , but for realistic time-dependent many-body dynamics this has been di cult to achieve. Here, we show how single shots can be simulated from numerical solutions of the time-dependent many-body Schrödinger equation. Using this approach, we provide first-principle explanations for fluctuations in the collision of attractive Bose-Einstein condensates (BECs), for the appearance of randomly fluctuating vortices and for the centre-of-mass fluctuations of attractive BECs in a harmonic trap. We also show how such simulations provide full counting distributions and correlation functions of any order. Such calculations have not been previously possible and our method is broadly applicable to many-body systems whose phenomenology is driven by information beyond what is typically available in low-order correlation functions.A postulate of quantum mechanics states that the positions r 1 , . . . , r N of N particles measured in an experiment are distributed according to the N -particle probability density P(r 1 , . . . , r N ) = |Ψ (r 1 , . . . , r N )| 2 , where Ψ (r 1 , . . . , r N ) is the manybody wavefunction of the system. In many experiments the positions of individual particles cannot be measured directly. Ultracold atom experiments provide a rare exception to this rule, which is why we focus on ultracold atoms in the following, but the concept is completely general. If Ψ (r 1 , . . . , r N ) is known, single experimental shots can be simulated by drawing the positions of all particles from P(r 1 , . . . , r N ), which results in a vector of positions (r 1 , . . . , r N ) that we refer to as a single shot. This has been realized for time-invariant many-body systems 1-4 . However, for time-dependent many-body systems it has remained a challenge. The difficulty stems from the fact that the functional form of the wavefunction is generally not known in many-body dynamics.Attempts at simulating single shots have been reported in the context of semiclassical dynamics: several authors have interpreted classical trajectories obtained within the truncated Wigner approximation as individual realizations of experiments 5,6 . Under the strict condition that the Wigner function is non-negative, some authors consider this interpretation plausible 7 or have fewer objections to it 8 . Here we show that this interpretation must also be dismissed for positive Wigner functions (see Supplementary Information). Although quantum Monte Carlo algorithms 9 sample the N -particle probability to obtain lower ground state energies, for time-dependent many-body systems not even the nodal structure of the wavefunction is known in advance, and hence quantum Monte Carlo methods are less suited. For further details see Supplementary Information.For sampling P(r 1 , . . . , r N ) it helps to realize that P(r 1 , . . . , r N ) = P(r 1 )P(r 2 |r 1...

Single-shot imaging of trapped Fermi gas

“…In a similar way the solitons emerge in a process of detection of N -particles prepared in a type II excited state of a 1D system of bosons interacting via short-range potential described by the Lieb-Linger model [9]. Single shot time-dependent simulations of many-body dynamics showing appearance of fluctuating vortices and center-ofmass fluctuations of attractive BEC have been reported recently [10]. …”

“…takes one of the values N = 1, 3,6,10,15. For open shells (not shown here) the patterns depend on the occupied orbitals at the Fermi level.…”

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“…In addition to the discussed dark soliton example, our results should be applicable to many other systems such as Bose gases in a doublewell potential [30], fragmenting bright solitons [12,13] or symmetrically colliding fragments in a harmonic trap [15,60]. If the central density turns out to be vanishing or too small such that g 2 (0, 0) becomes effectively ill-defined, the whole analysis has to be carried out in momentum space via long ToF measurements.…”

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