Quantum Breathing Mode of Trapped Particles: From Nanoplasmas to Ultracold Gases

Abstract

Particles spatially confined in trapping potentials have attracted increasing interest over the recent decade. Of particular importance are systems of charged particles, such as non-neutral plasmas, nanoplasmas, electrons in metal clusters, electrons in quantum-confined semiconductor structures ("artificial atoms"), electrons on the surface of liquid helium, ions in traps or highly charged particles (grains) in dusty plasmas. A second example of recent interest are systems with other kinds of pair interactions, including dipole interaction, which is important for excitons in quantum wells or ultracold Fermi and Bose gases in traps and optical lattices.Trapped systems are fundamentally different from macroscopic systems since they are dominated by strong spatial inhomogeneity and finite size effects (the properties depend on the exact particle number). Furthermore, by changing the strength of the confinement potential, the many-particle state of the system can be externally controlled-from weak coupling (gas-like) to strong coupling (crystal-like). While trapped classical particles are meanwhile well understood and accessible to first-principle computer simulations, their quantum counterparts still pose big challenges, both for experiment and theory. Therefore, collective properties that can be easily measured or computed and allow to diagnose the many-particle state of the system are of prime importance. It has been found that the quantum breathing mode (monopole oscillation) is one of the most important such properties. In recent years a number of theoretical studies has demonstrated that the quantum breathing mode is ideally suited to measure the coupling strength (the degree of nonideality) of a trapped system, its kinetic and interaction energy and other key observables. This give rise to a novel kind of "spectroscopy" of trapped systems.In this review these developments are summarized. The quantum breathing mode is studied for trapped fermions and bosons with Coulomb and dipole interaction, respectively. A systematic description of collective oscillations and especially the breathing mode is provided. Making use of time-dependent perturbation theory, it is shown how the corresponding breathing frequencies are connected to the properties of the initial equilibrium system. This gives rise to the application of the quantum mechanical sum rules. It is demonstrated how an improved version of the conventional sum rule formulas is suitable for an accurate description of the breathing mode in small systems. Finally, the dependence of the breathing mode on the particle number N is analyzed and the limit of large N is studied for one-dimensional and two-dimensional systems.

Quantum dynamical response of ultracold few-boson ensembles in finite optical lattices to multiple interaction quenches

“…The breathing mode refers to an expansion and con- traction of the bosonic cloud and can be excited by varying the interaction strength or the frequency of the trapping potential [43][44][45]. Here, due to the lattice symmetry it is expected [14,15] to be more prone in the central well.…”

Negative-quench-induced excitation dynamics for ultracold bosons in one-dimensional lattices

“…This mode has further been identified as a two-body intrawell collision which was dipole-like [15,16]. In addition, a local-breathing mode reminiscent to the usual breathing mode in a harmonic trap [17][18][19][20][21][22] has been observed. The occurrence of a resonance between a tunneling mode and the cradle giving rise to the controlabilibity between the inter and intrawell dynamics has also been revealed.…”

“…Shown are different components of the correlation function g (1) ij with respect to the left well g LM (green thin solid line) and g netic and interaction energy or the coupling strength [17][18][19]. It refers to an expansion and contraction of the bosonic cloud and can be excited either via a variation of the interparticle interaction or a modulation of the frequency of the trapping potential.…”

Finite-temperature quantum effects on confined charges

“…Focus on other properties such as spin polarization or coherent control of trap properties, charge dependence and others acceptable to direct observation can be addressed. For example, simple dynamical modes can be identified (a novel "spectroscopy" based on a quantum breathing mode has been proposed recently [39,40]). Smaller particle number and access to details of optical properties will require a more detailed specification of the quantum input, beyond Thomas-Fermi.…”