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Chains of quantum dots coupled to superconductors are promising for the realization of the Kitaev model of a topological superconductor. While individual superconducting quantum dots have been explored, control of longer chains requires understanding of interdot coupling. Here, double quantum dots are defined by gate voltages in indium antimonide nanowires. High transparency superconducting niobium titanium nitride contacts are made to each of the dots in order to induce superconductivity, as well as probe electron transport. Andreev bound states induced on each of dots hybridize to define Andreev molecular states. The evolution of these states is studied as a function of charge parity on the dots, and in magnetic field. The experiments are found in agreement with a numerical model., QN/Bakkers Lab, QuTech

Spontaneous symmetry breaking plays a key role in our understanding of nature. In a relativistic field theory, a broken continuous symmetry leads to the emergence of two types of fundamental excitations: 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 particles 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 becomes over-damped through coupling to Nambu-Goldstone modes has been a subject of theoretical debate. Here we reveal and study a Higgs mode in a two-dimensional neutral superfluid close to the transition to a Mott insulating phase. We unambiguously identify the mode by observing the expected softening of the onset of spectral response when approaching the quantum critical point. In this regime, our system is described by an effective relativistic field theory with a two-component quantum-field, constituting 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, which also addresses the consequences of reduced dimensionality and confinement of the system. Our work constitutes a first step in exploring emergent relativistic models with ultracold atomic gases.

We study nonequilibrium dynamics of ultracold two-component Fermi gases in low-dimensional geometries after the interactions are quenched from a weakly interacting to a strongly interacting regime. We develop a T-matrix formalism that takes into account the interplay between Pauli blocking and tight confinement in low-dimensional geometries. We employ our formalism to study the formation of molecules in quasi-two-dimensional Fermi gases near Feshbach resonance and show that the rate at which molecules form depends strongly on the transverse confinement. Furthermore, Pauli blocking gives rise to a sizable correction to the binding energy of molecules., Academy of Finland, United States. Army Research Office, United States. Defense Advanced Research Projects Agency. Optical Lattice Emulator Program, MIT-Harvard Center for Ultracold Atoms, National Science Foundation (U.S.) (Grant No.DMR-07-05472), United States. Air Force Office of Scientific Research (Quantum Simulation MURI), United States. Air Force Office of Scientific Research (MURI on Ultracold Molecules, United States. Army Research Office. Multidisciplinary University Research Initiative (ARO-MURI on Atomtronics)

We theoretically study the relaxation of high energy single particle excitations into molecules in a system of attractive fermions in an optical lattice, both in the superfluid and the normal phase. In a system characterized by an interaction scale U and a tunneling rate tau, we show that the relaxation rate scales as approximately Ctexp[-alphaU(2)/tau(2)In(U/tau)] in the large U/tau limit. We obtain explicit expressions for the temperature and density dependent exponent alpha, both in the low temperature superfluid phase and the high temperature phase with pairing but no coherence between the molecules. We find that the relaxation rate decreases both with temperature and deviation of the fermion density from half filling. We show that quasiparticle and phase degrees of freedom are effectively decoupled within experimental time scales allowing for observation of ordered states even at high total energy of the system., Pub. in Physical Review Letters, v107, p145303-1/145303-5, 2011. Sponsored in part by AFOSR and DARPA.

We consider a localized impurity atom that interacts with a cloud of fermions in the paired state. We develop an effective scattering length description of the interaction between an impurity and a fermionic atom using their vacuum scattering length. Treating the pairing of fermions at the mean-field level, we show that the impurity atom acts like a magnetic impurity in the condensed matter context, and leads to the formation of a pair of Shiba bound states inside the superconducting gap. In addition, the impurity atom can lead to the formation of deeply bound states below the Fermi sea., United States. Army Research Office, United States. Defense Advanced Research Projects Agency. Optical Lattice Emulator Program, MIT-Harvard Center for Ultracold Atoms, National Science Foundation (U. S.) (Grant no. DMR-07-05472), National Science Foundation (U. S.) (Grant no. PHY-06-53514), United States. Air Force Office of Scientific Research. Multidisciplinary University Research Initiative, United States. Air Force Office of Scientific Research. Young Investigator Program, United States. Army Research Office. Multidisciplinary University Research Initiative. Atomtronics, Alfred P. Sloan Foundation

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., United States. Army Research Office, United States. Defense Advanced Research Projects Agency (DARPA) (OLE program), Swiss National Science Foundation, National Science Foundation (U.S.) (DMR-07-05472), National Science Foundation (U.S.) (PHY-06-53514), United States. Air Force Office of Scientific Research (MURI), Alfred P. Sloan Foundation

We consider a localized impurity atom that interacts with a cloud of fermions in the paired state. We develop an effective scattering length description of the interaction between an impurity and a fermionic atom using their vacuum scattering length. Treating the pairing of fermions at the mean-field level, we show that the impurity atom acts like a magnetic impurity in the condensed matter context, and leads to the formation of a pair of Shiba bound states inside the superconducting gap. In addition, the impurity atom can lead to the formation of deeply bound states below the Fermi sea., United States. Army Research Office, United States. Defense Advanced Research Projects Agency. Optical Lattice Emulator Program, MIT-Harvard Center for Ultracold Atoms, National Science Foundation (U. S.) (Grant no. DMR-07-05472), National Science Foundation (U. S.) (Grant no. PHY-06-53514), United States. Air Force Office of Scientific Research. Multidisciplinary University Research Initiative, United States. Air Force Office of Scientific Research. Young Investigator Program, United States. Army Research Office. Multidisciplinary University Research Initiative. Atomtronics, Alfred P. Sloan Foundation

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., Sponsored in part by ARO and DARPA.