arXiv:1101.1901v1 [cond-mat.other] 10 Jan 2011 Rough chains superfluidity in a polarized gas of dipolar molecules B. Capogrosso-Sansone 1 and A.B. Kuklov 2 1 Institute for Theoretical Atomic, Molecular and Optical Physics, Harvard-Smithsonian Center of Astrophysics, Cambridge, MA, 02138 2 Department of Engineering Science and Physics, CSI, CUNY, Staten Island, NY 10314, USA (Dated: January 11, 2011) We study quantum chains in a gas of polar bosonic molecules confined in a stack of N identical 1d (cigar type) and 2d (plane type) optical lattice layers and polarized perpendicularly to the layers. A single chain quantum roughening transition is observed in ab initio simulations. It is proven that no superfluid of chains with length shorter than N is possible. Rough chain superfluid (RCSF) is found and analyzed within the J-current model approximation. A detection scheme is discussed. A possibility of RCSF in superstructures of indirect excitons is proposed. PACS numbers: 64.70.Tg, 05.30.Rt, 67.85.-d, 71.35.-y Quantum properties of extended objects – high energy strings (see in Ref.[1]), stripes in high-T c superconductors [2], vortices in superfluids and su- perconductors, dislocations in quantum crystals, etc. – are of great interest to many areas of physics. Self-assembly of classical dipolar molecules into chains has been investigated numerically in Ref. [3]. Successful trapping of high density samples of polar molecules [4] makes creating quantum chains a realistic possibility. Bose-Einstein condensation of stiff and non-interacting chains was considered in Ref.[5] (see also fermionic case in Refs.[6]). Here we have found off-diagonal long range or- der (ODLRO) in N -body density matrix of rough and interacting chains, that is, RCSF (see also preliminary report in Ref.[7]). It emerges from N -layered molecular superfluid (N-SF) through quantum phase transition (QPT) – continuous in 1d and discontinuous in 2d (for N> 2). Close to the transition intra-chain roughening dynamics and inter-chain molecular exchanges result in the chain effective thickness being much larger than a typical inter-molecular distance. Model: We consider a stack of N identical parallel to each other layers, each being (1d or 2d) optical lattice confining dipolar bosonic molecules polarized perpendicularly to the stack (along z -axis). Periodic boundary conditions (PBC) are utilized along all directions unless stated otherwise. Hubbard Hamiltonian H = −J  〈ij〉,α a † iα a jα + 1 2  iα;jγ V iα;jγ n iα n iγ , (1) is defined in terms of onsite creation-annihilation operators a † iα ,a jα ( Greek and Latin indexes label layers and sites within a layer, respectively), with J being intra-layer single boson tunneling (no inter-layer tunneling) and n iα = a † iα a iα denoting onsite density operator obeying the hard-core constraint. The dipolar interaction matrix V iα;jγ is characterized by strength V d = d 2 z /b 3 z , where d z stands for the induced dipole moment and b z denotes distance between two nearest layers. No ”short” chain superfluid. N-SF state is characterized by [U(1)] N broken symmetries, that is, by N (quasi-) condensed phases ϕ α of the U(1) order parameters in each layer. The RCSF of chains of length N has one U(1) broken symmetry with the only condensed phase being ϕ = ∑ α=1,2,...,N ϕ α . This means ODLRO in M -body density matrix D M , with M = N , and no ODLRO for any M<N . A uniform state [8] with ODLRO in D M ∗ , 1 <M ∗ <N (and no ODLRO in any D M ,M<M ∗ ) requires that a sum of M ∗ phases is condensed. As long as M ∗ <N , choices of such M ∗ phases can be done in, at least, N equivalent ways constraining all N phases to be condensed. This implies N-SF state, that is, ODLRO in D M=1 . Thus, a minimal ODLRO can form in either D N or D 1 . Single chain. Ab initio simulations within the Worm Algorithm (WA) [9] of one chain are performed for single dipole per layer with hard wall conditions imposed at the space edges ±L/2 of each layer, with PBC along imaginary time β = 1/T , where T stands for temperature. One of the particles is pinned at the origin, i.e., in the middle of the layer where it be-