Phonon-Mediated Casimir Interaction between Mobile Impurities in One-Dimensional Quantum Liquids

Abstract

Virtual phonons of a quantum liquid scatter off impurities and mediate a long-range interaction, analogous to the Casimir effect. In one dimension the effect is universal and the induced interaction decays as 1/r 3 , much slower than the van der Waals interaction ∼ 1/r 6 , where r is the impurity separation. The sign of the effect is characterized by the product of impurity-phonon scattering amplitudes, which take a universal form and have been seen to vanish for several integrable impurity models. Thus, if the impurity parameters can be independently tuned to lie on opposite sides of such integrable points, one can observe an attractive interaction turned into a repulsive one.PACS numbers: 67.10. Jn, 67.85.Pq, 42.50.Lc, 03.75.Kk The concept of zero-point energy has fascinated minds ever since the inception of quantum mechanics. Beyond being merely an inconsequential redefinition of the ground state energy, it was shown by Casimir [1] that changes in the zero-point energy can lead to observable forces between uncharged conducting plates. Going beyond simple planar geometries, recent developments in nanotechnology [2][3][4][5][6][7][8][9][10] have stimulated intense efforts to understand Casimir interactions between conducting objects of arbitrary shape [11,12].Zero-point fluctuations of the electromagnetic field constitute only one example of a much broader class of phenomena. Essentially any medium whose fluctuations display long-range correlations, e.g., media with a continuously broken symmetry and associated Goldstone mode(s) [13], induce long-range interactions between perturbing objects that modify the spectrum of fluctuations. A well-known example of such media is a superfluid whose Goldstone mode is the quantized sound mode or phonon. Although 4 He was the first system to exhibit the remarkable properties of superfluidity, recent advances in ultracold atom trapping and manipulation [14] have lead to an unprecedented ability to study ultraclean bosonic or fermionic superfluids subject to tunable spatial dimensionality, lattice configuration and interaction strength.Perturbing objects or impurities can be controllably introduced by transferring a fraction of atoms into a different hyperfine state [15][16][17], or by admixing a different atomic species [18][19][20][21]. As we show, such impurities immersed in an interacting cold atom environment is a particularly appealing setup. It gives rise to a long-range interaction, which we hereafter denote as the Casimir interaction, due to scattering of virtual phonons, the same mechanism lying at the heart of the analogous photoninduced Casimir effect. In addition, the cold-atom analog of the interaction has the advantage of being continuously tunable both in magnitude and in sign, a task which is hardly achievable in a linear electromagnetic medium [22].In most studies of Casimir interactions the analysis is restricted to static configurations of objects or bounding surfaces. The impurities in quantum liquids are typically free to propagate under the influence...

Observation of the Phononic Lamb Shift with a Synthetic Vacuum

“…We open up an avenue for benchmarking a new class of many-body theories, comprising not only different mutually interacting particles, but also interactions of their [45,46], as well as in dynamical situations [47][48][49]. By varying the distance between the lattice valleys, we could directly test the dependence of the energy shift on this spacing and therefore measure sign and amplitude of the vacuum-induced forces.…”

The Casimir-like effect in a one-dimensional Bose gas

“…We obtain an analytic expression for the interaction that interpolates between the two limiting behaviors. The obtained result does not require any regularization.Thus Schecter and Kamenev [12] were able to describe the Casimir-like interaction only at very large distances, ℓ?ξ. The contact interaction between impurities obtained in [12] is an artifact of the abovementioned limitation.An impurity that interacts repulsively with the particles of the liquid produces the depletion of the liquid density.…”

Oscillating Casimir potential between two impurities in a spin-orbit-coupled Bose-Einstein condensate

“…On the other hand, for 1D BEC at finite temperature, the quantum depletion becomes quite large, and the multi-phonon process can not be neglected. It is pointed out that, when the two-phonon exchanging process is included, the potential would become long-ranged [47]. We leave the SOC effect on the Casimir potential with multi-phonon process for the future study.…”