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Register a new userBose-Einstein condensation in a stiff TOP trap with adjustable geometry
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We report on the realisation of a stiff magnetic trap with independently adjustable trap frequencies, $omega_z$ and $omega_r$, in the axial and radial directions respectively. This has been achieved by applying an axial modulation to a Time-averaged Orbiting Potential (TOP) trap. The frequency ratio of the trap, $omega_z / omega_r$, can be decreased continuously from the original TOP trap value of 2.83 down to 1.6. We have transferred a Bose-Einstein condensate (BEC) into this trap and obtained very good agreement between its observed anisotropic expansion and the hydrodynamic predictions. Our method can be extended to obtain a spherical trapping potential, which has a geometry of particular theoretical interest.
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The asymptotic (non)equivalence of canonical and microcanonical ensembles, describing systems with soft and hard constraints respectively, is a central concept in statistical physics. Traditionally, the breakdown of ensemble equivalence (EE) has been associated with nonvanishing relative canonical fluctuations of the constraints in the thermodynamic limit. Recently, it has been reformulated in terms of a nonvanishing relative entropy density between microcanonical and canonical probabilities. The earliest observations of EE violation required phase transitions or long-range interactions. More recent research on binary networks found that an extensive number of local constraints can also break EE, even in absence of phase transitions. Here we study for the first time ensemble nonequivalence in weighted networks with local constraints. Unlike their binary counterparts, these networks can undergo a form of Bose-Einstein condensation (BEC) producing a core-periphery structure where a finite fraction of the link weights concentrates in the core. This phenomenon creates a unique setting where local constraints coexist with a phase transition. We find surviving relative fluctuations only in the condensed phase, as in more traditional BEC settings. However, we also find a non-vanishing relative entropy density for all temperatures, signalling a breakdown of EE due to the presence of an extensive number of constraints, irrespective of BEC. Therefore, in presence of extensively many local constraints, vanishing relative fluctuations no longer guarantee EE.
We have constructed a mm-scale Ioffe-Pritchard trap capable of providing axial field curvature of 7800 G/cm$^2$ with only 10.5 Amperes of driving current. Our novel fabrication method involving electromagnetic coils formed of hard anodized aluminum strips is compatible with ultra-high vacuum conditions, as demonstrated by our using the trap to produce Bose-Einstein condensates of 10$^6$ $^87$Rb atoms. The strong axial curvature gives access to a number of experimentally interesting configurations such as tightly confining prolate, nearly isotropic, and oblate spheroidal traps, as well as traps with variable tilt angles with respect to the nominal axial direction.
We discuss the effects of quenched disorder in a dilute Bose-Einstein condensate confined in a hard walls trap. Starting from the disordered Gross-Pitaevskii functional, we obtain a representation for the quenched free energy as a series of integer moments of the partition function. Positive and negative disorder-dependent effective coupling constants appear in the integer moments. Going beyond the mean-field approximation, we compute the static two-point correlation functions at first-order in the positive effective coupling constants. We obtain the combined contributions of effects due to boundary conditions and disorder in this weakly disordered condensate. The ground state renormalized density profile of the condensate is presented. We also discuss the appearance of metastable and true ground states for strong disorder, when the effective coupling constants become negative.
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