week ending 27 JUNE 2014
PHYSICAL REVIEW LETTERS
PRL 112, 255301 (2014)
Role of Quantum Fluctuations in the Hexatic Phase of Cold Polar Molecules 1
Wolfgang Lechner,1,2,* Hans-Peter Büchler,3 and Peter Zoller1,2
Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, 6020 Innsbruck, Austria 2 Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria 3 Institute for Theoretical Physics III, University of Stuttgart, D-70550 Stuttgart, Germany (Received 22 January 2014; revised manuscript received 17 March 2014; published 25 June 2014) Two-dimensional crystals melt via an intermediate hexatic phase, which is characterized by an anomalous scaling of spatial and orientational correlation functions and the absence of an attraction between dislocations. We propose a protocol to study the effect of quantum fluctuations on the nature of this phase with a model system of strongly correlated ultracold polar molecules. Dislocations can be located in experiment from local energy differences which induce internal stark shifts in the molecules. We present a criterion to identify the hexatic phase from the statistics of the end points of topological defect strings and find a hexatic phase, which is dominated by quantum fluctuations, between the crystal and superfluid phases. DOI: 10.1103/PhysRevLett.112.255301
PACS numbers: 67.85.−d, 61.72.Ff
The theory of the crystal-to-liquid transition in two dimensions by Kosterlitz, Thouless, Nelson, Halperin, and Young (KTHNY) has become a paradigm of melting in reduced dimensions [1–4]. The KTHNY theory predicts that the intermediate hexatic phase between crystal and liquid is connected to the microscopic mechanism of formation and dissociation of thermally activated dislocation pairs [5–10]. This results in the remarkable coexistence of short-range translational order and quasi–long range bond-orientational order observed in the hexatic phase. The role of quantum fluctuations in this transition and the possibility of dislocation pairs that are induced by quantum fluctuations is, however, an open question. A straightforward study of the scaling of correlation functions in the quantum regime is a theoretical and experimental challenge as enormous system sizes are required [7]. From an experimental point of view, the main challenge is the lack of controllable model systems where the parameter regime can be tuned in the full range from a classical crystal to a superfluid. With the remarkable recent progress in trapping and manipulating ensembles of ultracold molecules (e.g., LiCs [11] or NaK [12]) such a system may be in reach [13–26]. In this Letter, we present a theoretical study of the hexatic phase from the dynamics and interaction of dislocations, which are induced by an interplay of quantum and thermal fluctuations. We propose methods to study these effects in an experiment with cold polar molecules. Using numerical path-integral methods [27], we provide theoretical evidence for a hexatic phase between the crystal and superfluid from the interplay between quantum and thermal fluctuations. The hexatic phase is identified from the interaction between dislocations, which is measured from the statistics of the end points of defect strings [28]. These points are topologically protected dislocations which 0031-9007=14=112(25)=255301(5)
cannot annihilate and their interaction has a double-well shape [28]. We derive the critical value for the barrier height from elasticity theory which allows one to distinguish between the hexatic and crystalline phases. The defects can be identified in experiment from local energy differences of dislocation particles. We consider a two-dimensional dipolar system described by H¼
X p2 X D i : þ 2m r3 i i
PHYSICAL REVIEW LETTERS
PRL 112, 255301 (2014)
Role of Quantum Fluctuations in the Hexatic Phase of Cold Polar Molecules 1
Wolfgang Lechner,1,2,* Hans-Peter Büchler,3 and Peter Zoller1,2
Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, 6020 Innsbruck, Austria 2 Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria 3 Institute for Theoretical Physics III, University of Stuttgart, D-70550 Stuttgart, Germany (Received 22 January 2014; revised manuscript received 17 March 2014; published 25 June 2014) Two-dimensional crystals melt via an intermediate hexatic phase, which is characterized by an anomalous scaling of spatial and orientational correlation functions and the absence of an attraction between dislocations. We propose a protocol to study the effect of quantum fluctuations on the nature of this phase with a model system of strongly correlated ultracold polar molecules. Dislocations can be located in experiment from local energy differences which induce internal stark shifts in the molecules. We present a criterion to identify the hexatic phase from the statistics of the end points of topological defect strings and find a hexatic phase, which is dominated by quantum fluctuations, between the crystal and superfluid phases. DOI: 10.1103/PhysRevLett.112.255301
PACS numbers: 67.85.−d, 61.72.Ff
The theory of the crystal-to-liquid transition in two dimensions by Kosterlitz, Thouless, Nelson, Halperin, and Young (KTHNY) has become a paradigm of melting in reduced dimensions [1–4]. The KTHNY theory predicts that the intermediate hexatic phase between crystal and liquid is connected to the microscopic mechanism of formation and dissociation of thermally activated dislocation pairs [5–10]. This results in the remarkable coexistence of short-range translational order and quasi–long range bond-orientational order observed in the hexatic phase. The role of quantum fluctuations in this transition and the possibility of dislocation pairs that are induced by quantum fluctuations is, however, an open question. A straightforward study of the scaling of correlation functions in the quantum regime is a theoretical and experimental challenge as enormous system sizes are required [7]. From an experimental point of view, the main challenge is the lack of controllable model systems where the parameter regime can be tuned in the full range from a classical crystal to a superfluid. With the remarkable recent progress in trapping and manipulating ensembles of ultracold molecules (e.g., LiCs [11] or NaK [12]) such a system may be in reach [13–26]. In this Letter, we present a theoretical study of the hexatic phase from the dynamics and interaction of dislocations, which are induced by an interplay of quantum and thermal fluctuations. We propose methods to study these effects in an experiment with cold polar molecules. Using numerical path-integral methods [27], we provide theoretical evidence for a hexatic phase between the crystal and superfluid from the interplay between quantum and thermal fluctuations. The hexatic phase is identified from the interaction between dislocations, which is measured from the statistics of the end points of defect strings [28]. These points are topologically protected dislocations which 0031-9007=14=112(25)=255301(5)
cannot annihilate and their interaction has a double-well shape [28]. We derive the critical value for the barrier height from elasticity theory which allows one to distinguish between the hexatic and crystalline phases. The defects can be identified in experiment from local energy differences of dislocation particles. We consider a two-dimensional dipolar system described by H¼
X p2 X D i : þ 2m r3 i i
