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arXiv:1201.4784 · Physical Review Letters

Excitation Spectrum of a Supersolid

Sebastiano Saccani, Saverio Moroni, Massimo Boninsegni

Published Apr 24, 2012• 148 citations
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Abstract

Conclusive experimental evidence of a supersolid phase in any known condensed matter system is presently lacking. On the other hand, a supersolid phase has been recently predicted for a system of spinless bosons in continuous space, interacting via a broad class of soft-core, repulsive potentials. Such an interaction can be engineered in assemblies of ultracold atoms, providing a well-defined pathway to the unambiguous observation of this fascinating phase of matter. In this Letter, we study by first principles computer simulations the elementary excitation spectrum of the supersolid, and show that it features two distinct modes, namely, a solidlike phonon and a softer collective excitation, related to broken translation and gauge symmetry, respectively.

DOI
10.1103/physrevlett.108.175301

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Conclusive experimental evidence of a supersolid phase in any known condensed matter system is presently lacking. On the other hand, a supersolid phase has been recently predicted for a system of spinless bosons in continuous space, interacting via a broad class of soft-core, repulsive potentials. Such an interaction can be engineered in assemblies of ultracold atoms, providing a well-defined pathway to the unambiguous observation of this fascinating phase of matter. In this Letter, we study by first principles computer simulations the elementary excitation spectrum of the supersolid, and show that it features two distinct modes, namely, a solidlike phonon and a softer collective excitation, related to broken translation and gauge symmetry, respectively.
By means of a mean-field method, we have studied the zero-temperature structure and excitation spectrum of a three-dimensional soft-core bosonic system for a value of the interaction strength that favors a crystal structure made of atomic nanoclusters arranged with fcc ordering. In addition to the longitudinal and transverse phonon branches expected for a normal crystal, the excitation spectrum shows a soft mode related to the breaking of gauge symmetry, which signals a partial superfluid character of the solid. Additional evidence of supersolidity is provided by the calculation of the superfluid fraction, which shows a first-order drop, from 1 to 0.4, at the liquid-supersolid transition and a monotonic decrease as the interaction strength parameter is increased. The conditions for the coexistence of the supersolid with the homogeneous superfluid are discussed, and the surface tension of a representative solid-liquid interface is calculated.
The low temperature phase diagram of an assembly of Bose particles, interacting via a simple soft disc potential, is studied numerically by means of Monte Carlo simulations. At sufficiently high densities, the system features a cluster crystal phase, as observed in its classical counterpart. In the low temperature limit, and in a relatively wide region of parameter space, the quantum cluster crystal undergoes a transition to a supersolid phase, displaying both a finite superfluid fraction and crystalline order. We argue that soft-core Bosons ought be regarded as a ‘minimal model’ of continuous-space supersolidity. With the aim of elucidating the interplay between superfluid response and solid order, we compute the excitation spectrum of the system. A comparison of that of the insulating cluster crystal with that of the supersolid, shows that the latter features an additional acoustic mode.
We investigate the zero-temperature excitation spectrum of two-dimensional soft-core bosons for a wide range of parameters and across the phase transition from a superfluid to a supersolid state. Based on mean-field calculations and recent quantum Monte Carlo results, we demonstrate the applicability of the Bogoliubov-de Gennes equations, even at high interaction strengths where the system forms an insulating cluster crystal. Interestingly, our study reveals that the maximum energy of the longitudinal phonon band in the supersolid phase connects to the maxon energy of the superfluid at the phase transition.
More than 40 years ago, Andreev, Lifshitz and Chester suggested the possible existence of a peculiar solid phase of matter, the microscopic constituents of which can flow superfluidly without resistance due to the formation of zero-point defects in the ground state of self-assembled crystals. Yet, a physical system where this mechanism is unambiguously established remains to be found, both experimentally and theoretically. Here we investigate the zero-temperature phase diagram of two-dimensional bosons with finite-range soft-core interactions. For low particle densities, the system is shown to feature a solid phase in which zero-point vacancies emerge spontaneously and give rise to superfluid flow of particles through the crystal. This provides the first example of defect-induced, continuous-space supersolidity consistent with the Andreev–Lifshitz–Chester scenario. The peculiar supersolid phase of matter was predicted several decades ago, yet a physical system where it exists remains to be found. Cinti et al.investigate the zero-temperature phase diagram of bosons interacting by soft-core potentials and find that defects in it can give rise to a supersolid phase.
We study the spectrum of elementary excitations of a dipolar Bose gas in a three-dimensional anisotropic trap across the superfluid-supersolid phase transition. Theoretically, we show that, when entering the supersolid phase, two distinct excitation branches appear, respectively associated with dominantly crystal and superfluid excitations. These results confirm infinite-system predictions, showing that finite-size effects play only a small qualitative role, and connect the two branches to the simultaneous occurrence of crystal and superfluid orders. Experimentally, we probe compressional excitations in an Er quantum gas across the phase diagram. While in the Bose-Einstein condensate regime the system exhibits an ordinary quadrupole oscillation, in the supersolid regime we observe a striking two-frequency response of the system, related to the two spontaneously broken symmetries.
Bose-Einstein condensation is a macroscopic quantum phenomenon where cooling down a gas of bosonic particles to ultracold temperatures results in the macroscopic occupation of the lowest energy state. This new state of matter has been used as a quantum simulator of many-body phenomena and theories due to its extreme tunability and controllability. An important example of such a many-body system is the polaron which, in its most general form, describes an impurity interacting with a bosonic bath. In the case of ultracold Bose gases, the impurity interacts with and is dressed by the Bogoliubov excitations of the gas. A supersolid is a state of matter that exhibits both superfluidity and crystalline order, which are seemingly irreconcilable properties. It has recently been observed in dipolar ultracold Bose gases, where it arises from the long-range anisotropic dipole-dipole interactions, and also other systems. The breaking of both translational symmetry and gauge symmetry results in multiple excitation modes in the supersolid. In this thesis, the charged Bose polaron and an impurity in a dipolar ultracold Bose gas exhibiting supersolidity (the supersolid Bose polaron) are studied. The ground-state properties of the charged Bose polaron are discussed using a variational path-integral approach. Absorption spectroscopy is proposed as a probe of the charged Bose polaron, and the optical response is studied for weak impurity-boson interactions. Next, the one-dimensional dipolar supersolid Bose polaron is investigated where multiple approaches are used for the derivation of the ground-state properties. The study of the polaron problem with a supersolid background is of particular interest because of the rich excitation spectrum of the supersolid. Interesting phenomena, such as possible localization of the polaron to a single droplet for strong interactions, are observed. The absorption spectrum of a charged impurity in the supersolid is also derived, which, because of the different excitation modes of the supersolid, shows multiple peaks from which information such as the superfluid fraction may be obtained.