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Atoms and Molecules: Assessment and Perspective CondensedCondensed--mattermatter physics with ultracold atoms and molecules: assessment and perspective Dan Stamper-Stamper-KurnKurn UC Berkeley, Physics Lawrence Berkeley National Laboratory, Materials Sciences a humble assessment of >15 years of studying CM physics with ultracold atoms Are we pushing the boundaries of what is possible? Creating model systems and controlling quantum matter • cavity optomechanics Are we discovering? Creating/discovering novel materials; addressing the “quantum many-body physics problem” • resonant Ferm i gases Novel many-body quantum physics far from equilibrium • quantum quenches Are we producing technological and economic benefit? Ultracold-atom magnetometers structural matters Growth and saturation? Fun ding for an inter disc ip linary fie ld Training for an interdisciplinary field Physicists are control freaks Superconducting electronics Mesoscopic electronics “qubit” “artificial atom” reservoir of mobile electrons Schoelkopf, Mooij, Martinis = “artificial metal” Goldhaber-Gordon Quantum dots Exhibit/study/test physical principles most directly Frontiers are good place to make discoveries 5 nm Awschalom −20 Z 10 m LIGO: Laser Interferometer peak sensitivity: Gravitational-wave Observatory fractional expansion (strain) of ~ 10-23 in 1 s The scientific challenge: extremely sensitive position (force) detection One paradigm for cavity opto-opto-mechanicsmechanics L Detection Zff φ = hκ Z force per photon: H =++HHH − Zf n hc osc cav in/ out f = λL Cavity frequency shift due to Optical force on oscillator oscillator d ispl acement (sensitivity to oscillator motion) (measurement back-action on oscillator) Common goals: Dominance of quantum fluctuations over thermal fluctuations cooling mechanical oscillator to ground state reaching quantum limits for sensitivity Study and use quantum effects quantifying measurement backaction squeezed light (pondermotive squeezing) entanglement of macroscopic object with light isolation from thermal environment Common means: Better isolation from environment Colder starting points Stronger optomechanical coupling Kippenberg and Vahala, Science 321, 1172 (2008) Cavity optomechanics with ultracold atoms Berkeley Esslinger, Esslinger, Zürich Optomechanics with SiN membranes Harris, Yale; now others too ϕ = 2kZCoM Nature 452, 72 (2008) 2 HEom=−()2sin2cos2ϕϕ nf( ) Znfk CoM −( ϕ) Zn CoM +K linear coupling: qu adratic cou pling: optical spring, bistability, phonon QND,… ponderomotive squeezing… δ z many atoms in a trap i “mechanical” potential z0 light-atom coupling ωz =−2π ( 20 200 kHz) g()zg= 0 sin( kzp ) T < μK phonon # 0.3 ωZ gz2 ( ˆ ) ⎡⎤Zˆ 2 h i ˆˆ(0)ˆ ˆCMCoM 2 ˆ HnnFZnFknom=Δ−−∑ h Nsin( 2ϕ ) CoM cos( 2ϕσ)⎢ +⎥ atoms Δca ⎣ N ⎦ Tunability of optomechanical coupling (strength, type) Immediately in the quantum regime (ultracold(ultracold)) Dominated by quantum radiation pressure fluctuations (thermally isolated) Connected directly to basic theory (quantum optics, atomic physics) Measuring radiation pressure forces Δca > 0 g()zg= 0 sin( kzp ) probe light repels atoms “Coherent” effect: Optical forces in ththee cavity will displace the trapped atoms Probing the cavity shifts the cavity resonance ⇒ nonlinear cavity optics [PRL 99, 213601 (2007)] “Incoherent” effect: Quantum force fluctuations ⇒ momentum diffusion Atoms act as intracavity sensor of photon number fluctuations momentumomentumm diffusion = quantum backactionof position measurement [Nature Physics 4, 561 (2008)] Quantum optics: intracavity photon shot noise spectrum For a coherently driven cavity: 21n Spectral power density of S ()ω ∝ nn κ 2 2 photon number fluctuations 1/+Δ−()ω κ (inter alia, force fluctuations) spectrum analyzer Δ Quantum measurement: backaction of position measurement Z cavity outputs reflect itω Eein =η cavity field Ecav ⎡⎤iFZ FZ EEZ(0)1 Δ=ωω − + cav cav =+⎢ ⎥ 0 ⎣ κ −Δi h ⎦ h 2 Information iFZ per photon: Matches force fluctuation κ −Δi h spectrum (as it must) Δ CavityCavity--inducedinduced heating: measured by atom loss dE− dN NUkT=−() dtB dt 1 kT≈ U B 10 CavityCavity--inducedinduced heating: measured by atom loss Heating rate per cavity photon compared to free space value What this means: Quantum fluctuations of radiation pressure dominate over other heating sources Quantum metrology: back-back-actionaction heating of macroscopic object at level prescribed by quantum measurement limits Granular regime of optomechanics define dimensionless granularity parameter: Z zerozero--pppoint position sp read ε = SQL δ Z = κ h F measurement uncertainty from single photon Does a singgple photon measure the cantilever to better than the SQ L? 1 F × (single(single--photonphoton force) x (residence time of photon) ε = κ h zerozero--pointpoint momentum spread ZSQL Does a singgple photon’s kick sig nificantly yp perturb the cantilever? CantileverCantilever--basedbased optomechanicsoptomechanics:: ε = 10--77 ––1010--55 Atomsoms--bdbased opthitomechanicscs:: ε = 0010.01 – 10 a humble assessment of >15 years of studying CM physics with ultracold atoms Are we pushing the boundaries of what is possible? Creating model systems and controlling quantum matter • cavity optomechanics Are we discovering? Creating/discovering novel materials; addressing the “quantum many-body physics problem” • resonant Ferm i gases Novel many-body quantum physics far from equilibrium • quantum quenches Are we producing technological and economic benefit? Ultracold-atom magnetometers structural matters Growth and saturation? Fun ding for an inter disc ip linary fie ld Training for an interdisciplinary field What does discovering look like? Iron-based SC: Topological insulators: “experimental discovery” “theoretical discovery” Parent compounds identified 2006 – 2008 From 2D QSH effect to 3D concept 2007 Flurry of synthesis + reports Suggestions lead to ARPES observations Focused experimental probing + in Bi materials theoretical development Topological superconductors, classifications, suggested applications Feshbach Resonances Scattering Length 3 z] [x10 a0 ] 1 20 rgy [MH ee En 10 0 0 bound state -10 Atoms form Isolated atom pairs stable molecules are unstable -1 -20 650 834.15 Magnetic Field [G] The BEC-BCS Crossover Thanks to Martin Zwierlein for slides Experimental realization Zwierlein, Ketterle Jin Studied using techniques benchmarked from prior BEC research: Hydrodynamics of expanding gas (Thomas et al.) Collective excitations ((,Grimm, Salomon ) Vortices and critical velocity (Ketterle) Photoassociation (Hulet) … and newly developed/refined techniques RF spectroscopy (Grimm, Jin, Ketterle) Noise correlations (Jin) Shina Tan’s relations Universal thermodynamics… Many properties of the interacting Fermi gas are determined by high- momentum portion of the 2-body wave-function Pk = C () k 4 C = “Contact” such as… Local density of pairs (related to photoassociation rate) Sum of kinetic and interaction energy Change in total energy due to small adia bat ic change in scattering lengt h Virial relation between total energy and potential energy in harmonic trap Relation between pressure and total energy Inelilastic two-bdbody loss rate (aga in relates to didensity of pairs ) Clock shift in RF transitions S. Tan, Ann. Phys 323, 2952, 2971, and 2987 (2008) Shina Tan’s relations: experimental verification “Verification of universal relations in a strongly interacting Fermi gas,” Stewart et al (Jin group), preprint arXiv:1002.1987 Change in total energy due to small adiabatic change in scattering length measure the contact, then test… Virial relation between total energy and potential energy in harmonic trap see also Hu et al. (Vale group), preprint arXiv:1001.3200 New material: spinor Bose gas 37 electrons mF = 2 Energy J = 1/2 mF = 1 F=2 mF = 0 Optically magnetically mF = -1 trapped F=2 trappable m = -2 spinor gas F mF = -1 F=1 mF = 0 Optically m = 1 37 protons F trapped F=1 50 neutrons spinor gas I = 3/2 B rrur F =+IJ Phases and symmetries 2 ur 2 EcnFqF=−2 + z ferromagnetic states unmagnetized state longitudinal axis transverse plane Z2 ×U (1) SO(2)× U (1) U (1) BEC 0 q qcn02= 2 Quantum quench: Non-equilibrium (quantum) dynamics at a (quantum) phase transition Spontaneous ferromagnetism M φ • inhomogeneously broken symmetry • ferromagnetic domains, llargearge aandnd ssmallmall • unmagnetized domain walls marking rapid reorientation φ M Thold = 30 60 90 120 150 180 210 ms Quantum (?) spin fluctuations and quantum (?) spin amplifiers quantum spin gain of quantum -limited fluctuation (variance) of fluctuations parametric amplifier macroscopic spin texture saturation log(Var(M)) = seed x gain log(G( 0)) quantify seed by image noise extrapolation time after quench Quantum quench theory: Lamacraft, PRL 98, 160404 (2007); expt: PRA 79, 043631 (2009) a humble assessment of >15 years of studying CM physics with ultracold atoms Are we pushing the boundaries of what is possible? Creating model systems and controlling quantum matter • cavity optomechanics Are we discovering? Creating/discovering novel materials; addressing the “quantum many-body physics problem” • resonant Ferm i gases Novel many-body quantum physics far from equilibrium • quantum quenches Are we producing technological and economic benefit? Ultracold-atom magnetometers structural matters Growth and saturation? Fun ding for an inter disc ip linary fie ld Training for an interdisciplinary field Spinor gas magnetometry B N atoms F F F φ Probe: t = 0 t = τ Budker and Romalis, Nature Phys. 3, 227 (2007) N N φ0 φ0 N N ΔB φ0 φ1 N N φ0 φ0 t = 0 t = τ “Field” measurements B AC
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