Monitoring and manipulating Higgs and Goldstone modes in a supersolid quantum gas

Abstract

Access to collective excitations lies at the heart of our understanding of quantum many-body systems. We study the Higgs and Goldstone modes in a supersolid quantum gas that is created by coupling a Bose-Einstein condensate symmetrically to two optical cavities. The cavity fields form a U(1)-symmetric order parameter that can be modulated and monitored along both quadratures in real time. This enables us to measure the excitation energies across the superfluid-supersolid phase transition, establish their amplitude and phase nature, as well as characterize their dynamics from an impulse response. Furthermore, we can give a tunable mass to the Goldstone mode at the crossover between continuous and discrete symmetry by changing the coupling of the quantum gas with either cavity.Collective excitations are crucial for describing the dynamics of quantum many-body systems. They provide unified explanations of phenomena studied in different disciplines of physics, such as in condensed matter [1] or particle physics [2], or in cosmology [3]. The symmetry of the underlying effective Hamiltonian determines the character of the excitations, which changes in a fundamental way when a continuous symmetry is broken at a phase transition. Excitations can now appear both at finite and zero energy.In the paradigmatic case of models with U(1)-symmetry breaking, the system can be described by a complex scalar order parameter in an effective potential as illustrated in Fig. 1(A-B) [4]. In the normal phase, the potential is bowl-shaped with a single minimum at vanishing order parameter, and correspondingly two orthogonal amplitude excitations. Within the ordered phase, the potential shape changes to a 'sombrero' with an infinite number of minima on a circle. Here, fluctuations of the order parameter reveal two different excitations: a Higgs (or amplitude) mode, which stems from amplitude fluctuations of the order parameter and shows a finite excitation energy, and a Goldstone (or phase) mode, which stems from phase fluctuations of the order parameter and has zero excitation energy. The former should yield correlated fluctuations in the two squared quadratures of the order parameter, whereas the latter should show anticorrelated behavior.Condensed matter systems typically do not provide access to both quadratures of the order parameter, and Higgs and Goldstone modes have to be excited and detected by incoherent processes. In addition, the idealized situation is often disguised by further interactions that reduce the number of distinct modes [1, 6]. For charged particles, the minimal coupling to a vector potential can even completely suppress the Goldstone mode through the Anderson-Higgs mechanism [2]. In chargedensity wave compounds, a persisting Higgs mode has been observed as a well-defined resonance [7][8][9]. In superfluid Helium [10] and Bose-Einstein condensates [11] * donner@phys.ethz.ch Illustration of the experiment. A Bose-Einstein condensate (blue stripes) cut into slices by a transverse pump lattice potential (red stripes)...

Introduction to the Dicke Model: From Equilibrium to Nonequilibrium, and Vice Versa

“…At the interface between these two phases the model shows an enlarged U(1) symmetry, [145,146] as realized experimentally recently. [147,148] Such experiments have prompted theoretical discussion of the possibility of a vestigial ordered phase, [149] where the two cavities become phase locked but without superradiance, as well as the nature of the excitations close to the U(1) symmetric point. [150] A further extension in this direction leads to multimode cavities, which give rise to spatially varying, cavity-mediated interactions among the atoms.…”

Tunable-Range, Photon-Mediated Atomic Interactions in Multimode Cavity QED

“…These interactions may be sufficiently strong to create novel quantum phases of matter [4]. Indeed, single-and few-mode cavity QED in the optical domain have already provided demonstrations of supersolidity [5,6] and exotic Mott physics [7,8], in addition to supermode-density-wave-polariton condensation [9]. Moreover, the driven-dissipative, openquantum-system nature of cavity QED can change the character of quantum phase transitions, providing a new window into quantum nonequilibrium physics [10,11].…”

“…[9] in the regime of a few degenerate modes. Two crossed single-mode cavities with a BEC coupled to both was shown to exhibit a Uð1Þ symmetry in the superradiant, self-organization phase as well as a Higgs mode [5,6]. Though BECs were employed in the latter two experiments, the number of modes was insufficient to mediate short-range interactions.…”

Quantum simulation of strongly correlated condensed matter systems

“…Alternatively, self-organization transitions due to infinitely long-range effective interactions arise in degenerate quantum gases interacting with an optical cavity [221], where ordered states and collective excitations in the presence of additional two-particle interactions [222] and coupling to multiple cavities [223] are currently under active investigation.…”