Bose-Einstein Condensates  

In General > s.a. gas [boson gas]; quantum phase transitions [including fermion condensation].
* Idea: Bose-Einstein condensation is a phase transition of a boson gas, consisting in the amalgamation of many bosonic atoms so cold and dense (chilled to nearly 0 K) that they act as a single quantum state, essentially a single "superparticle"; This occurs when T is so low that the atoms' de Broglie wavelength becomes comparable to the distance between them; Similar to Cooper pairs in superconductors.
* History, theory: Started with S N Bose's letter to Einstein in 1924, after his paper was rejected by Philosophical Magazine; Einstein extended the ideas to massive particles in 1925; Viewed with skepticism (how can you have condensation in an ideal gas, without forces, no applications, ...) until 1938, when F London proposed it to explain He superfluidity, discovered in 1928.
* History, experiment: 1995, First produced with a trapped atomic gas of 5 million Rb atoms, directly observable; 2001, Nobel prize for physics given for Bose-Einstein condensation in dilute gases of alkali atoms; 1998, Observed in H atoms (at T ≈ 40 μK, with about 100 million atoms); 2003, Observed in Ytterbium, which differs from most of the elements that had previously been condensed because it has two valence electrons rather than one, and can be prepared in a non-magnetic state; 2005, Observed in Chromium, which has a very large magnetic dipole moment.
* Properties: Enormous indices of refraction.
@ Books: Pitaevskii & Stringari 03; Annett 04 [intro]; Griffin et al 09; in Chang & Ge 17.
@ General references: Scharf AJP(93)sep; Cornell & Wieman SA(98)mar; Ketterle PT(99)dec [experiments]; Burnett et al PT(99)dec [theory]; Collins SA(00)dec; Yukalov PLA(06) [self-consistent theory]; Yukalov PPN(11)-a1105 [rev]; Ferrari EJP(11) [pedagogical]; Tsubota et al PRP(13) [rev]; Bao a1403-proc [mathematical models and numerical methods, rev]; Liebert & Schilling PRR(21)-a2010 [one-particle reduced density matrix approach].
@ Dynamics: Schlein a0704-proc; Caspar et al PRA(16)-a1511 [dissipative]; Davis et al a1601-ch [BEC formation and dynamics of phase transitions].
@ Perturbations: Barceló et al PRD(10)-a1006 [quasiparticles and quantization]; Kurita et al PRA(10)-a1007 [particle creation]; Prain et al PRD(10)-a1009 [expanding BEC]; Chatterjee & Diakonis JPA(14)-a1306 [thermal fluctuations]; Wang et al PRL(15) [with electrons in Rydberg states].
@ Related topics: Dorlas et al JSP(05)mp [and long cycles]; Schützhold PRL(06) [accurate phonon detection]; Healey FP(11)-a0910 [Gedanken-experiments, reduction and emergence]; Dalton AP(11) [interferometry and decoherence]; Gagatsos et al OSID(13)-a1207 [and mutual information]; Andreev a2007 [hydrodynamics beyond the mean-field approximation]; > s.a. geometric phase; Gross-Pitaevskii Equation; unruh effect.
@ Applications: focus Phy(14) [ultraprecise measurements]; > s.a. monopoles; quantum computation; rotations; solid matter [supersolids].

Gravity-Related Topics > s.a. gravitational-wave detection and propagation; semiclassical quantum gravity.
@ General references: Fagnocchi et al NJP(10)-a1001 [relativistic BECs]; news pw(10)jun [BECs in free fall]; Rivas & Camacho MPLA(11)-a1101 [in a homogeneous gravitational field]; Akant et al a1306 [on a manifold with non-negative Ricci curvature]; Mukherjee et al PRD(15)-a1409 [constraints on condensate stars]; Schroven et al PRD(15)-a1507, Brito et al PLB(16)-a1508 [self-gravitating BECs]; Chavanis & Matos EPJP-a1606 [hydrodynamic approach].
@ And black holes: Kühnel & Sundborg a1401 [as graviton condensates, with extra dimensions]; > s.a. black-hole analogs.
@ And neutron stars: Gruber & Pelster EPJD(14)-a1403 [at finite temperature]; Pethick et al a1507-in.
@ As dark matter: Lundgren et al ApJL(10)-a1001 [ultra-light scalar particles]; Harko JCAP(11)-a1105 [condensation in dwarf galaxies]; Harko & Mocanu PRD(12)-a1203 [cosmological evolution]; Dwornik et al proc(14)-a1210 [and galactic rotation curves]; Bettoni et al JCAP(14)-a1310 [relativistic BEC on a curved background]; Li et al PRD(14)-a1310 [constraints]; Diez-Tejedor et al PRD(14)-a1404 [in dwarf spheroidal galaxies]; Das & Bhaduri CQG(15)-a1411 [gravitons, and dark energy]; Cohen-Tannoudji AFLB-a1507 [Mach's ether and the QCD vacuum]; Harko et al JCAP-a1510 [at galaxy cluster scales]; Capolupo AHEP(16)-a1608 [and dark energy]; Zhang et al EPJC(18)-a1804 [galactic halos]; Das & Bhaduri a1808-pn [rev]; Castellanos et al IJMPD(20)-a1910 [test]; Rindler-Daller a2104 [quantum-coherent dark matter in the Milky Way]; > s.a. types of dark matter.
@ Spacetime as a condensate: Gielen PRD(15)-a1411 [perturbations]; Cadoni et al PRD(18)-a1801 [de Sitter space]; > s.a. emergent gravity.
@ In cosmology: Gielen CQG(14)-a1404 [loop quantum gravity]; Erdem & Gültekin JCAP(19)-a1908 [mechanism].
@ As analog systems: Bravo et al EPJQT-a1406 [and gravitational waves, quantum simulation]; Leizerovitch & Reznik a1711 [Kaluza-Klein fields]; Eckel et al PRX(18) [expanding universe model]; > s.a. wormholes.
> And quantum gravity: see gravitating many-body systems; lorentz symmetry breaking; matter in quantum gravity; GUP phenomenology.

Other Models and Examples > s.a. atomic physics; effective field theories; light; sound; temperature; vacuum [fluctuation].
* Examples: Superfluid \({}^3\)He and superconducting metals contain BECs of fermion pairs.
* And interactions: In 1947 Nikolay Bogoliubov developed a theory to describe interacting BECs, and he predicted the fraction of atoms that remains in the BEC as a function of the strength of the interactions between them; 2017, The predictions of the theory have been experimentally confirmed.
@ Specific types of gases: news pn(95)jul, pn(95)aug, pn(98)nov, pn(99)jun, Bradley et al PRL(95) [atoms]; Wynar et al Sci(00)feb + pn(00)feb [Rb\(^~_2\) molecules]; Hall AJP(03)jul [trapped dilute gases, RL]; Takasu et al PRL(03) [in Yb]; Grether et al PRL(07) [relativistic ideal Bose gas]; Stellmer et al PRL(09), Martínez et al PRL(09) + Zelevinsky Phy(09) [84Sr]; Deng et al RMP(10), Snoke & Littlewood PT(10)aug [polariton gas, towards room temperature]; Hainzl & Seiringer LMP(12) [gas of fermion pairs, described by the Gross-Pitaevskii functional]; Halder et al PRA(12) [two-electron atoms]; Zhang et al a2006 [molecular].
@ Theoretical models: Damski & Zurek PRL(07) [spin-1, quantum phase transition]; Kurita et al PRA(09) [inhomogeneous, in curved-spacetime analog]; Jaeck et al JSP(09)-a0905 [in random external potentials]; Dolgov et al JCAP(09) [non-zero temperature model electrodynamics]; Kawaguchi & Ueda PRP(12) [spinor BECs]; Castellanos & Chacón-Acosta PLB(13)-a1301 [1D polymers, using lqg effective Hamiltonian]; Bolte & Kerner proc(15)-a1403 [on quantum graphs]; Castellanos et al IJTP(17)-a1605 [polymer quantization]; Kanda RVMP(17)-a1705 [on graphs].
@ For photons: news PT(11)feb [experiments with photons and molecules in an optical cavity]; Kirton & Keeling PRL(13) [non-equilibrium model]; Schmitt et al PRL(14) [observation of grand-canonical number statistics]; Cheng a1412 [in the universe]; Mendonça & Terças PRA(17)-a1704 [in a plasma]; Nyman & Walker JMO(18)-a1706 [by scattering from a fluorescent dye in a microcavity]; Müller PRA(19)-a1801 [framework].
@ And interactions: Smith et al PRL(11) [effect of interactions]; Lopes et al PRL(17) [confirming Bogoliubov's theory]; de Oliveira & Michelangeli RVMP(19)-a1811 [two-component condensates].
@ 2D: Cho et al NJP(15)-a1409; Viebahn et al PRL(19) + Santos Phy(19) [on a 2D quasicrystal optical lattice]; Caraci et al a2011 [Gross-Pitaevskii regime].
@ Other systems: Petrellis et al AP(11)-a1105 [N bosons + 1 fermion]; Berges & Sexty PRL(12) [relativistic field theories far from equilibrium]; Carusotto et al NJP(13) [atomic and solid-state physics]; Finazzi & Carusotto PRA(14)-a1309 [atomic, entangled phonons]; Lee et al NJP(15)-a1409 [composite bosons, quantum-information approach]; > s.a. Zitterbewegung.
@ Related topics: Reichel SA(05)feb [and microchips]; Lye et al PRL(05) [in a random potential]; Balewski et al Nat(13)oct-a1306 [coupled to a single electron]; news pw(13)ul [faster, all-laser cooling process]; Berezhiani & Khoury PRD(19)-a1812 [emergent long-range interactions]; news pt(20)jun, sn(20)jun [Rb BEC's in the Cold Atom Lab on the ISS].
> Generalizations: see Fermi-Einstein Condensation.

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