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Victor Gurarie University of Colorado Boulder Synthetic Quantum Matter 2 New field in Quantum Many Body Physics: Arose Over the Last 20 Years

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Victor Gurarie University of Colorado Boulder Synthetic Quantum Matter 2 New field in Quantum Many Body Physics: Arose Over the Last 20 Years 1 Dynamics & Entanglement in Synthetic UQM Victor Gurarie University of Colorado Boulder Synthetic quantum matter 2 New field in quantum many body physics: arose over the last 20 years Can be loosely split into: 1. Bottom-up engineering: using elements 2. Hamiltonian engineering: a gas of cold designed to perform as quantum degrees atoms with adjustable interactions, placed of freedom to build up a quantum many in external “trap” or optical lattices, with body systems. Superconducting qubits, random potential. cold ions. Advantage over more conventional solid state systems: 1. Hamiltonian is known precisely. Can be used as “quantum simulators”. 2. Precise accounting over degrees of freedom. Can be fully isolated from the environment. Can easily be driven out of equilibrium or prepared in an arbitrary state. 3. Detailed probes: measures of momentum distribution, spatial density distribution; harder to measure transport articles depth of around 13 Er the interference maxima no longer increase in which is of the order of 2 ms for a lattice with a potential depth of 9 strength (see Fig. 2e): instead, an incoherent background of atoms Er. A signi®cant degree of phase coherence is thus already restored gains more and more strength until at a potential depth of 22 Er no on the timescale of a tunnelling time. interference pattern is visible at all. Phase coherence has obviously It is interesting to compare the rapid restoration of coherence been completely lost at this lattice potential depth. A remarkable coming from a Mott insulator state to that of a phase incoherent feature during the evolution from the coherent to the incoherent state, where random phases are present between neighbouring state is that when the interference pattern is still visible no broad- lattice sites and for which the interference pattern also vanishes. ening of the interference peaks can be detected until they completely This is shown in Fig. 3b, where such a phase incoherent state is vanish in the incoherent background. This behaviour can be created during the ramp-up time of the lattice potential (see Fig. 3 articles explained on the basis of the super¯uid±Mott insulator phase legend) and where an otherwise identical experimental sequence is diagram. After the system has crossed the quantum critical point used. Such phase incoherent states can be clearly identi®ed by U=J z 3 5:8, it will evolve in the inhomogeneous case into adiabatically mapping the population of the energy bands onto alternating regions of incoherent Mott insulator phases and coher- the Brillouin zones19,21. When we turn off the lattice potential Quantum phase transition from a ent super¯uid phases2, where the super¯uid fraction continuously adiabatically, we ®nd that a statistical mixture of states has been decreases for increasing ratios U/J. created, which homogeneously populates the ®rst Brillouin zone of Restoring coherence super¯uid to a Mott insulator in A notable property of the Mott insulator state is that phase coherence can be restored very rapidly when the optical potential is lowered again to a value where the ground state of the many-body a system is completely super¯uid. This is shown in Fig. 3. After only 22 ) agasofultracoldatoms 4 ms of ramp-down time, the interference pattern is fully visible r E again, and after 14 ms of ramp-down time the interference peaks ( 0 9 have narrowed to their steady-state value, proving that phase V È τ = 20 ms Markus Greiner*, Olaf Mandel*, Tilman Esslinger², Theodor W. Hansch* & Immanuel Bloch* coherence has been restored over the entire lattice. The timescale for the restoration of coherence is comparable to the tunnelling time 0 * Sektion Physik, Ludwig-Maximilians-UniversitaÈt, Schellingstrasse 4/III, D-80799 Munich, Germany, and Max-Planck-Institut fuÈr Quantenoptik, D-85748 Garching, 80 ms 20 ms t t =J between two neighbouring lattice sites in the system, 3 Time Germany tunnel ~ articles b 125 ² Quantenelektronik, ETH ZuÈrich, 8093 Zurich, Switzerland First quantum-simulated state (2002) ............................................................................................................................................................................................................................................................................ m) for the local occupation ni of atoms on a single lattice site is period of 500 ms to nrad 24 Hz such that a spherically symmetric µ 100 poissonian, that is, its variance is given by Var n nà . Further- Bose±Einstein condensate with a Thomas±Fermi diameter of For a system at a temperature of absolute zero,i all thermali ¯uctuations are frozen out, while quantum ¯uctuations prevail. These articlesz more, this state is well described by a macroscopic wavefunctionh i 26 mm is present in the magnetic trapping potential. microscopic quantum ¯uctuations can induce a macroscopic phase transition in the ground state of a many-body system when the 75 relativewith long-range strength of phase two coherence competing throughout energy terms the lattice.is varied across a criticalIn order value. to Here form we the observe three-dimensional such a quantum lattice phase potential, transition three If interactions dominate the hamiltonian, the ¯uctuations in optical standing waves are aligned orthogonal to each other, with x y in a Bose±Einstein condensate with repulsive interactions, held in a three-dimensional optical lattice potential. As the potential atom number of a Poisson distribution become energetically very their crossingQuantum point positioned at phase the centre of the transition Bose±Einstein from a 2 ᐜk 50 depth of the lattice is increased, a transition is observed from a super¯uid to a Mott insulator phase. In the super¯uid phase, each costly and the ground state of the system will instead consist of condensate. Each standing wave laser ®eld is created by focusing a atom is spread out over the entire lattice, with long-range phase coherence. But in the insulating phase, exact numbers of atoms localized atomic wavefunctions with a ®xed number of atoms per laser beamsuper¯uid to a waist of 125 mm at the to position a of Mott the condensate. insulator A in Width of central peak ( 25 aresite localized that minimize at individual the interaction lattice sites, energy. with The no many-body phase coherence ground acrosssecond the lens lattice; and a mirror this phase are then is characterized used to re¯ect the by laser a gap beam in the back excitationstate is then spectrum. a product We of local can Fock induce states reversible for each changes lattice site. between In this theonto two itself, ground creating states the of standing the system. wave interference pattern. The agasofultracoldatoms 0 limit, the ground state of the many-body system for a commensu- lattice beams are derived from an injection seeded tapered ampli®er 0 2 4 6 8 10 12 14 rate ®lling of n atoms per lattice site in the homogeneous case is and a laser diode operating at a wavelength of l 852 nm. All t (ms) Markus Greiner*, Olaf Mandel*, Tilman Esslinger², Theodor W. HaÈnsch* & Immanuel Bloch* Agiven physical by: system that crosses the boundary between two phases (herebeams between are spatially kinetic ®ltered and interaction and guided energy) to the is experiment fundamental using to 4 cd e changes its properties in a fundamentalM way. It may, for example, quantumoptical ®bres.* phaseSektion Acousto-optical Physik, transitions Ludwig-Maximilians-Universitaand modulators inherentlyÈt, Schellingstrasse different are used 4/III, tofrom D-80799 control normal Munich, the Germany, and Max-Planck-Institut fuÈr Quantenoptik, D-85748 Garching, ² n Germany melt or freeze. This macroscopicjªMI J0 ~ change aÃi isj0 driven by microscopic 3 phase transitions, which are usually driven by the competition Figure 1 Schematic three-dimensional interference pattern with measured absorption i & i intensity² ofQuantenelektronik, the lattice beams ETH ZuÈrich, and 8093 introduce Zurich, Switzerland a frequency difference of ¯uctuations. When the temperaturei of1 the system approaches zero, between inner energy and entropy. images taken along two orthogonal directions. The absorption images were obtained after about 30............................................................................................................................... MHz between different standing wave laser ®elds................................................................................................................................ The .............. Hamiltonian engineering: ballistic expansion from a lattice with a potential depth of V 10E and a time of ¯ight of all thermalThis Mott ¯uctuations insulator die state out. cannot This be prohibits described phase by transitionsa macroscopic in polarizationThe physics of of a standing the above-described wave laser ®eld system is chosen is captured to be linear by the and 0 r 1 15 ms. classicalwavefunction systems like at zero in temperature, a Bose condensed as their phase, opportunity and thus to change is not Bose±HubbardorthogonalFor a polarized system model at a, which totemperature all describes other of absolute standing an interacting zero, waves. all thermal boson Due ¯uctuations gasto the in are frozen out, while quantum ¯uctuations prevail. These has vanished. However, their quantum mechanical counterparts can a lattice potential.microscopic The quantum hamiltonian ¯uctuations in cansecond induce quantized a macroscopic form phase reads: transition in the ground state of a many-body
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