Two-dimensional scattering and bound states of polar molecules in bilayers

Klawunn, M.; Pikovski, Alexander; Santos, Luís

doi:10.1103/physreva.82.044701

Cited by 76 publications

(121 citation statements)

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“…This method is associated with strong relaxation losses [28], although nonconservative three-body interactions can also lead to interesting effects [20,29]. This Letter is motivated by the observation that dipolar particles trapped on a single layer and oriented perpendicular to the plane repel each other, whereas in a bilayer configuration there is always a bound state [30][31][32][33][34]. We argue that the bound state emerges from the scattering continuum as one gradually splits the layer into two and reduces the interlayer tunneling amplitude below a critical value t = t c .…”

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confidence: 99%

“…E ↑↑ E ↑↓ are determined from the ZR boundary conditions: φ ↑↑ (r) ∝ ln( E ↑↑ re γ /2) and φ ↑↓ (r) ∝ ln( E ↑↓ re γ /2), where γ ≈ 0.5772 is the Euler constant, E ↑↑ = 4 exp(−6γ)r −2 * [37], and E ↑↓ ≈ 4 exp(−8/r 2 * ) [33,34,38]. f zr (0) vanishes for exponentially small t = t c = E ↑↓ E ↑↑ /4 ∝ exp(−4/r 2 * ).…”

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confidence: 99%

“…The bound state in the potential V ↑↓ [30][31][32][33][34]36] is a true eigenstate of our model in the limit t → 0. Its wave function contains only the φ ↑↓ part; i.e., the two dipoles are localized on different layers.…”

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Three-Body Interacting Bosons in Free Space

Petrov

2014

Phys. Rev. Lett.

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We propose a method of controlling two-and three-body interactions in an ultracold Bose gas in any dimension. The method requires us to have two coupled internal single-particle states split in energy such that the upper state is occupied virtually but amply during collisions. By varying system parameters one can switch off the two-body interaction while maintaining a strong threebody one. The mechanism can be implemented for dipolar bosons in the bilayer configuration with tunneling or in an atomic system by using radio-frequency fields to couple two hyperfine states. One can then aim to observe a purely three-body interacting gas, dilute self-trapped droplets, the paired superfluid phase, Pfaffian state, and other exotic phenomena.PACS numbers: 34.50. 05.30.Jp, The Feshbach resonance technique, which allows for tuning the two-body interaction to any value, has been a major breakthrough in the field of quantum gases [1]. Reaching strongly interacting regimes by using this method is proven successful in two-component fermionic mixtures [2] because of the naturally built-in mechanism of suppression of local three-body inelastic processes [3]: the Pauli principle prohibits three fermions to be close to each other as at least two of them are identical. Essentially the same mechanism is responsible for the repulsion between weakly bound molecules in this system ensuring the mechanical stability. Bosons, having no such protection, are much more fragile. A Bose-Einstein condensate (BEC) collapses in free space even for infinitesimally weak attraction [4] not to mention devastating recombination losses close to resonance [5,6].A repulsive three-body force can stabilize the system and induce nontrivial many-body effects. A weakly interacting BEC with two-body attraction (coupling constant g 2 < 0) and three-body repulsion (g 3 > 0) is predicted to be a droplet, the density of which in the absence of external confinement and neglecting the surface tension is flat and equals n = −3g 2 /2g 3 [7][8][9]. For a strong (beyond mean-field) two-body attraction the spinless Bose gas can pass from the atomic to paired superfluid phase via an Ising-type transition with peculiar topological properties [10][11][12]. However, the mechanical stability of the system requires repulsive few-body interactions [13] or other stabilizing mechanisms [14]. Few-body forces are also important for quantum Hall problems: the exact ground state of bosons in the lowest Landau level with a repulsive three-body contact interaction is the Pfaffian state [15] also known as the weak-pairing phase and characterized by non-Abelian excitations [16]. Interestingly, a finite range of the three-body interaction breaks the pairing [17]. On the other hand, there may be a transition from the weak-to strong-pairing Abelian phase [18], presumably driven by varying g 2 .Most proposals for generating effective three-body interactions deal with lattice systems [19][20][21][22][23][24]. In free space, since three-body effects are significant when g 3 n is of order g 2...

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Three-Body Interacting Bosons in Free Space

Petrov

2014

Phys. Rev. Lett.

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“…However, it has been proven that V (r) always has a bound state [17], at any dimensionless strength β = r * /λ, with r * = md 2 / 2 being the dipole-dipole length. For β ≪ 1 the binding energy is exponentially small [19]:…”

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Interlayer Superfluidity in Bilayer Systems of Fermionic Polar Molecules

et al. 2010

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We consider fermionic polar molecules in a bilayer geometry where they are oriented perpendicularly to the layers, which permits both low inelastic losses and superfluid pairing. The dipole-dipole interaction between molecules of different layers leads to the emergence of interlayer superfluids. The superfluid regimes range from BCS-like fermionic superfluidity with a high Tc to Bose-Einstein (quasi-)condensation of interlayer dimers, thus exhibiting a peculiar BCS-BEC crossover. We show that one can cover the entire crossover regime under current experimental conditions. PACS numbers: 03.75.Ss, Ultracold gases of dipolar particles attract great interest because the dipole-dipole interaction drastically changes the nature of quantum degenerate regimes compared to ordinary short-range interacting gases [1,2]. This has been demonstrated in experiments with Bosecondensed chromium atoms which have a magnetic moment of 6µ B equivalent to an electric dipole moment of 0.05 D [3][4][5]. The recent experiments on creating polar molecules in the ground ro-vibrational state [6,7] and cooling them towards quantum degeneracy [6] have made a breakthrough in the field. For such molecules polarized by an electric field the dipole-dipole interaction is several orders of magnitude larger than for atomic magnetic dipoles. This opens fascinating prospects for the observation of new quantum phases [1,2,[8][9][10][11][12]. The main obstacle is the decay of the system due to ultracold chemical reactions, such as KRb+KRb⇒K 2 +Rb 2 found in JILA experiments [13]. These reactions are expected to be suppressed by the intermolecular repulsion in 2D geometries where the molecules are oriented perpendicularly to the plane of their translational motion [14].In this Letter we consider fermionic polar molecules in a bilayer geometry where the dipoles are oriented perpendicularly to the layers (Fig. 1), which leads to low inelastic losses and allows for the possibility of superfluid pairing. The interaction between dipoles of different layers may lead to the emergence of an interlayer superfluid, that is a superfluid 2D gas where Cooper pairs are formed by fermionic molecules of different layers. We show that the interlayer dipole-dipole interaction provides a higher superfluid transition temperature than that for 2D spin-1/2 fermions with attractive short-range interaction.Interestingly, an increase in the interlayer dipole-dipole coupling leads to a novel BCS-BEC crossover resembling that studied for atomic fermions near a Feshbach resonance [15,16]. The reason is that two dipoles belonging to different layers can always form a bound state [17]. As long as the binding energy ǫ b is much smaller than the Fermi energy E F , or equivalently the size of the interlayer two-body bound state greatly exceeds the intermolecular spacing in the {x, y} plane, the ground state of the system is the BCS-paired interlayer superfluid. Once a reduction of the interlayer spacing λ or an increase of the molecular dipole moment d by an electric field make ǫ b >> E...

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“…These problems can be overcome in low-dimensional geometries where the dipolar particles are confined to either twodimensional (2D) planes or one-dimensional (1D) tubes with and without the presence of lattice potentials. A number of interesting predictions have been made for the phases of system with dipolar interactions, including exotic superfluids [15][16][17][18][19] , Luttinger liquids [20][21][22][23][24][25] , Mott insulators 26,27 , interlayer pairing [28][29][30][31] , non-trivial quantum critical points 32,33 , modified confinement-induced resonances [34][35][36][37] , roton modes and stripe instabilities [38][39][40][41][42][43][44][45] , and crystallization [46][47][48][49][50][51][52][53][54] , as well as formation of chain complexes [55][56][57][58][59][60]…”

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confidence: 99%

Dipoles on a two-leg ladder

Gammelmark¹,

Zinner²

2013

Phys. Rev. B

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We study polar molecules with long-range dipole-dipole interactions confined to move on a two-leg ladder for different orientations of the molecular dipole moments with respect to the ladder. Matrix product states are employed to calculate the many-body ground state of the system as function of lattice filling fractions, perpendicular hopping between the legs, and dipole interaction strength. We show that the system exhibits zig-zag ordering when the dipolar interactions are predominantly repulsive. As a function of dipole moment orientation with respect to the ladder, we find that there is a critical angle at which ordering disappears. This angle is slightly larger than the angle at which the dipoles are non-interacting along a single leg. This behavior should be observable using current experimental techniques.

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Two-dimensional scattering and bound states of polar molecules in bilayers

Cited by 76 publications

References 25 publications

Three-Body Interacting Bosons in Free Space

Three-Body Interacting Bosons in Free Space

Interlayer Superfluidity in Bilayer Systems of Fermionic Polar Molecules

Dipoles on a two-leg ladder

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