Universal Relations for Identical Bosons from Three-Body Physics

Braaten, Eric; Kang, Daekyoung; Platter, Lucas

doi:10.1103/physrevlett.106.153005

Cited by 136 publications

(198 citation statements)

References 24 publications

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“…[56,58] considered rf spectroscopy of fermions, but in the expression above, exchange statistics only enter through n(k). Interestingly, the large-momenta structure of n(k), which determines the high-frequency rf response, is insensitive to exchange statistics [57,76] and allows us to directly generalize the argument for bosons. In particular, for large momenta n(k) displays a universal power-law tail [52,53,57,77] …”

Section: A Generic Features Of the Rf Responsementioning

confidence: 99%

Radio-frequency spectroscopy of polarons in ultracold Bose gases

Shashi¹,

Grusdt²,

Abanin³

et al. 2014

Phys. Rev. A

111

182

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Recent experimental advances enabled the realization of mobile impurities immersed in a Bose-Einstein condensate (BEC) of ultracold atoms. Here, we consider impurities with two or more internal hyperfine states, and study their radio-frequency (rf) absorption spectra, which correspond to transitions between two different hyperfine states. We calculate rf spectra for the case when one of the hyperfine states involved interacts with the BEC, while the other state is noninteracting, by performing a nonperturbative resummation of the probabilities of exciting different numbers of phonon modes. In the presence of interactions, the impurity gets dressed by Bogoliubov excitations of the BEC, and forms a polaron. The rf signal contains a δ-function peak centered at the energy of the polaron measured relative to the bare impurity transition frequency with a weight equal to the amount of bare impurity character in the polaron state. The rf spectrum also has a broad incoherent part arising from the background excitations of the BEC, with a characteristic power-law tail that appears as a consequence of the universal physics of contact interactions. We discuss both the direct rf measurement, in which the impurity is initially in an interacting state, and the inverse rf measurement, in which the impurity is initially in a noninteracting state. In the latter case, in order to calculate the rf spectrum, we solve the problem of polaron formation: a mobile impurity is suddenly introduced in a BEC, and dynamically gets dressed by Bogoliubov phonons. Our solution is based on a time-dependent variational ansatz of coherent states of Bogoliubov phonons, which becomes exact when the impurity is localized. Moreover, we show that such an ansatz compares well with a semiclassical estimate of the propagation amplitude of a mobile impurity in the BEC. Our technique can be extended to cases when both initial and final impurity states are interacting with the BEC.

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Section: A Generic Features Of the Rf Responsementioning

confidence: 99%

Radio-frequency spectroscopy of polarons in ultracold Bose gases

Shashi¹,

Grusdt²,

Abanin³

et al. 2014

Phys. Rev. A

111

182

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“…In bosonic systems the high momentum tail of the momentum distribution contains a 1/k 5 correction due to three body contact [20]. We note that such correction is to be expected in nuclear systems, as three nucleon coalescence is not forbidden by the Pauli exclusion principle.…”

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confidence: 98%

Nuclear Neutron-Proton Contact and the Photoabsorption Cross Section

2015

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The nuclear neutron-proton contact is introduced, generalizing Tan's work, and evaluated from medium energy nuclear photodisintegration experiments. To this end we reformulate the quasideuteron model of nuclear photodisintegration and establish the bridge between the Levinger constant and the contact. Using experimental evaluations of Levinger's constant we extract the value of the neutron-proton contact in finite nuclei and in symmetric nuclear matter. Assuming isospin symmetry we propose to evaluate the neutron-neutron contact through measurement of photonuclear spin correlated neutron-proton pairs.PACS numbers: 05.30.Fk, Introduction -Considering a system of two-component fermions interacting via a short range interaction, Tan [1, 2] has established a series of relations between the amplitude of the high-momentum tail of the momentum distribution n σ (k), where σ is the spin, and the properties of the system, such as the energy, pair correlations and pressure. These relations, commonly known as the "Tan relations", are expressed through a new variable the "Contact" C = lim k→∞ k 4 n σ (k). The contact, being a state variable depends on the density of the system (usually expressed through the Fermi momentum k F ), its temperature, composition, and its thermodynamic state. The Tan relations are universal, they hold for few-body as well as for many-body systems, for ground state and for finite temperature, for normal state but also for superfluid state. Their validity range depends on the interparticle distance d ∝ 1/k F and the magnitude of the scattering length being both much larger than the potential range, usually characterized by the effective range r eff .The theoretical discovery of the Tan relations has led to a concentrated experimental effort to measure and verify them in ultracold atomic systems, where the scattering length as well as the density can be controlled. These efforts have led to experimental verification of Tan's relations in fermionic 40 K [3, 4] and 6 Li [5][6][7] systems. It was also found that the measured value of the contact, as function of (k F a) −1 along the BCS-BEC crossover, is in accordance with the theoretical predictions of [6].In this manuscript we focus on nuclear systems. Generalizing Tan's work, we introduce the nuclear contacts and present an experimental evaluation of the neutron-proton contact in finite nuclei and also in symmetric nuclear matter. To this end we relate the contact to medium energy photonuclear cross-section and utilize available experimental data. In ultracold atomic physics the ratio between the interparticle distance 1/k F , the scattering length a, and r eff can be controlled in such a way as to ensure that the a r eff and k F r eff 1. The nuclear two-body scattering length is about 5.38 fm when the two nucleons are in the 3 S 1 state and about -20 fm when they

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“…2(inset); however, a 1/κ 4 tail may exist below our detection limit at large κ where the signal-to-noise ratio is poor. In addition, three-body interactions could modify the high-momentum tail at unitarity [34].…”

mentioning

confidence: 99%

Universal dynamics of a degenerate unitary Bose gas

et al. 2014

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From neutron stars to high-temperature superconductors, strongly interacting many-body systems at or near quantum degeneracy are a rich source of intriguing phenomena. The microscopic structure of the first-discovered quantum fluid, superfluid liquid helium, is difficult to access due to limited experimental probes. While an ultracold atomic Bose gas with tunable interactions (characterized by its scattering length, a) had been proposed as an alternative strongly interacting Bose system [1][2][3][4][5][6][7][8] , experimental progress [9][10][11][12] has been limited by its short lifetime. Here we present time-resolved measurements of the momentum distribution of a Bose-condensed gas that is suddenly jumped to unitarity, i.e. to a = ∞. Contrary to expectation, we observe that the gas lives long enough to permit the momentum to evolve to a quasi-steady-state distribution, consistent with universality, while remaining degenerate. Investigations of the time evolution of this unitary Bose gas may lead to a deeper understanding of quantum many-body physics.A powerful feature of atom gas experiments that provides access to these new regimes is the ability to change the interaction strength using a magnetic-field Feshbach resonance [13]. In particular, at the resonance location, a is infinite. For atomic Fermi gases [14][15][16][17][18][19][20], accessing this regime by adiabatically changing a led to the achievement of superfluids of paired fermions and enabled investigation of the crossover from superfluidity of weakly bound pairs, analogous to the Bardeen-Cooper-Schrieffer (BCS) theory of superconductors, to Bose-Einstein condensation (BEC) of tightly bound molecules [16,17]. For bosonic atoms, however, this route to strong interactions is stymied by the fact that three-body inelastic collisions increase as a to the fourth power [21][22][23]. This circumstance has limited experimental investigation of Bose gases with increasing interaction strength to studying either non-quantum-degenerate gases [24,25] or BECs with modest interaction strengths (na 3 < 0.008, where n is the atom number density) [9][10][11][12].The problem is that the loss rate scales as n 2 a 4 while the equilibration rate scales as na 2 v, where v is the average velocity. Thus, it would seem that the losses will always dominate as a is increased to ∞. Even if we were to forsake thermal equilibrium and suddenly change a in order to project a weakly interacting BEC onto strong interactions [12,[26][27][28], one might expect that three-body losses would still dominate the ensuing dynamics for large a. In this work, however, we use this approach to take a BEC to the unitary gas regime, and we observe dynamics that in fact saturate on a timescale shorter than that set by three-body losses and that exhibit universal scaling with density.

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Universal Relations for Identical Bosons from Three-Body Physics

Cited by 136 publications

References 24 publications

Radio-frequency spectroscopy of polarons in ultracold Bose gases

Radio-frequency spectroscopy of polarons in ultracold Bose gases

Nuclear Neutron-Proton Contact and the Photoabsorption Cross Section

Universal dynamics of a degenerate unitary Bose gas

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