David Pekker

The ‘Higgs’ amplitude mode at the two-dimensional superfluid/Mott insulator transition

Spontaneous symmetry breaking plays a key role in our understanding of nature. In relativistic quantum field theory, a broken continuous symmetry leads to the emergence of two types of fundamental excitation: massless Nambu–Goldstone modes and a massive ‘Higgs’ amplitude mode. An excitation of Higgs type is of crucial importance in the standard model of elementary particle physics, and also appears as a fundamental collective mode in quantum many-body systems. Whether such a mode exists in low-dimensional systems as a resonance-like feature, or whether it becomes overdamped through coupling to Nambu–Goldstone modes, has been a subject of debate. Here we experimentally find and study a Higgs mode in a two-dimensional neutral superfluid close to a quantum phase transition to a Mott insulating phase. We unambiguously identify the mode by observing the expected reduction in frequency of the onset of spectral response when approaching the transition point. In this regime, our system is described by an effective relativistic field theory with a two-component quantum field, which constitutes a minimal model for spontaneous breaking of a continuous symmetry. Additionally, all microscopic parameters of our system are known from first principles and the resolution of our measurement allows us to detect excited states of the many-body system at the level of individual quasiparticles. This allows for an in-depth study of Higgs excitations that also addresses the consequences of the reduced dimensionality and confinement of the system. Our work constitutes a step towards exploring emergent relativistic models with ultracold atomic gases.

Observation of Elastic Doublon Decay in the Fermi-Hubbard Model

We investigate the decay of highly excited states of ultracold fermions in a three-dimensional optical lattice. Starting from a repulsive Fermi-Hubbard system near half filling, we generate additional doubly occupied sites (doublons) by lattice modulation. The subsequent relaxation back to thermal equilibrium is monitored over time. The measured absolute doublon lifetime covers 2 orders of magnitude. In units of the tunneling time h/J it is found to depend exponentially on the ratio of on-site interaction energy U to kinetic energy J. We argue that the dominant mechanism for the relaxation is a simultaneous many-body process involving several single fermions as scattering partners. A many-body calculation is carried out using diagrammatic methods, yielding fair agreement with the data.

Amplitude / Higgs Modes in Condensed Matter Physics

The order parameter and its variations in space and time in many different states in condensed matter physics at low temperatures are described by the complex function Ψ(r, t). These states include superfluids, superconductors, and a subclass of antiferromagnets and charge density waves. The collective fluctuations in the ordered state may then be categorized as oscillations of phase and amplitude of Ψ(r, t). The phase oscillations are the Goldstone modes of the broken continuous symmetry. The amplitude modes, even at long wavelengths, are well defined and are decoupled from the phase oscillations only near particle-hole symmetry, where the equations of motion have an effective Lorentz symmetry, as in particle physics and if there are no significant avenues for decay into other excitations. They bear close correspondence with the so-called Higgs modes in particle physics, whose prediction and discovery are very important for the standard model of particle physics. In this review, we discuss the theory and...

Individual topological tunnelling events of a quantum field probed through their macroscopic consequences

Measurements of the distribution of stochastic switching currents in homogeneous, ultra-narrow superconducting nanowires provide strong evidence that the low-temperature current-switching in such systems occurs through quantum phase slips—topological quantum fluctuations of the superconducting order parameter via which tunnelling occurs between current-carrying states.

Hilbert-Glass Transition: New Universality of Temperature-Tuned Many-Body Dynamical Quantum Criticality

Conventional phase transitions are usually characterized by a change in a fundamental thermodynamic observable, e.g., in density when liquid changes to vapor. A theoretical study of a one-dimensional disordered quantum spin chain reveals a new class of quantum phase transitions that leave no such signatures and pins down their origin.

Competition between pairing and ferromagnetic instabilities in ultracold Fermi gases near Feshbach resonances.

We study the quench dynamics of a two-component ultracold Fermi gas from the weak into the strong interaction regime, where the short time dynamics are governed by the exponential growth rate of unstable collective modes. We obtain an effective interaction that takes into account both Pauli blocking and the energy dependence of the scattering amplitude near a Feshbach resonance. Using this interaction we analyze the competing instabilities towards Stoner ferromagnetism and pairing.

Finding Matrix Product State Representations of Highly Excited Eigenstates of Many-Body Localized Hamiltonians

A key property of many-body localized Hamiltonians is the area law entanglement of even highly excited eigenstates. Matrix product states (MPS) can be used to efficiently represent low entanglement (area law) wave functions in one dimension. An important application of MPS is the widely used density matrix renormalization group (DMRG) algorithm for finding ground states of one-dimensional Hamiltonians. Here, we develop two algorithms, the shift-and-invert MPS (SIMPS) and excited state DMRG which find highly excited eigenstates of many-body localized Hamiltonians. Excited state DMRG uses a modified sweeping procedure to identify eigenstates, whereas SIMPS applies the inverse of the shifted Hamiltonian to a MPS multiple times to project out the targeted eigenstate. To demonstrate the power of these methods, we verify the breakdown of the eigenstate thermalization hypothesis in the many-body localized phase of the random field Heisenberg model, show the saturation of entanglement in the many-body localized phase, and generate local excitations.

Magnetic-field enhancement of superconductivity in ultranarrow wires.

We study the effect of an applied magnetic field on sub-10-nm wide MoGe and Nb superconducting wires. We find that magnetic fields can enhance the critical supercurrent at low temperatures, and do so more strongly for narrower wires. We conjecture that magnetic moments are present, but their pair-breaking effect, active at lower magnetic fields, is suppressed by higher fields. The corresponding microscopic theory, which we have developed, quantitatively explains all experimental observations, and suggests that magnetic moments have formed on the wire surfaces.

BCS-BEC crossover in bilayers of cold fermionic polar molecules

We investigate the quantum and thermal phase diagram of fermionic polar molecules loaded in a bilayer trapping potential with perpendicular dipole moment. We use both a BCS-theory approach that is most reliable at weak coupling and a strong-coupling approach that considers the two-body bound dimer states with one molecule in each layer as the relevant degree of freedom. The system ground state is a Bose-Einstein condensate (BEC) of dimer bound states in the low-density limit and a paired superfluid (BCS) state in the high-density limit. At zero temperature, the intralayer repulsion is found to broaden the regime of BCS-BEC crossover and can potentially induce system collapse through the softening of roton excitations. The BCS theory and the strongly coupled dimer picture yield similar predictions for the parameters of the crossover regime. The Berezinskii-Kosterlitz-Thouless transition temperature of the dimer superfluid is also calculated. The crossover can be driven by many-body effects and is strongly affected by the intralayer interaction which was ignored in previous studies.

Inherent stochasticity of superconductor-resistor switching behavior in nanowires.

We study the stochastic dynamics of superconductive-resistive switching in hysteretic current-biased superconducting nanowires undergoing phase-slip fluctuations. We evaluate the mean switching time using the master-equation formalism, and hence obtain the distribution of switching currents. We find that as the temperature is reduced this distribution initially broadens; only at lower temperatures does it show the narrowing with cooling naively expected for phase slips that are thermally activated. We also find that although several phase-slip events are generally necessary to induce switching, there is an experimentally accessible regime of temperatures and currents for which just one single phase-slip event is sufficient to induce switching, via the local heating it causes.