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Breaking the symmetry of a Brownian motor with symmetric potentials
Umeå University, Faculty of Science and Technology, Department of Physics.
Umeå University, Faculty of Science and Technology, Department of Physics.
Umeå University, Faculty of Science and Technology, Department of Physics.
2011 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, Vol. 44, no 15, 155002- p.Article in journal (Refereed) Published
Abstract [en]

The directed transport of Brownian particles requires a system with an asymmetry and with non-equilibrium noise. Here we investigate numerically alternative ways of fulfilling these requirements for a two-state Brownian motor, realized with Brownian particles alternating between two phase-shifted, symmetric potentials. We show that, besides the previously known spatio-temporal asymmetry based on unequal transfer rates between the potentials, inequalities in the potential depths, the frictions, or the equilibrium temperatures of the two potentials also generate the required asymmetry. We also show that the effects of the thermal noise and the noise of the transfer's randomness depend on the way the asymmetry is induced.

 

Place, publisher, year, edition, pages
Institute of Physics , 2011. Vol. 44, no 15, 155002- p.
National Category
Other Physics Topics
Research subject
Physics
Identifiers
URN: urn:nbn:se:umu:diva-42554DOI: 10.1088/1751-8113/44/15/155002OAI: oai:DiVA.org:umu-42554DiVA: diva2:409581
Available from: 2011-04-14 Created: 2011-04-08 Last updated: 2011-05-16Bibliographically approved
In thesis
1. Ultracold atoms in optical potentials: from noise-induced transport to superfluidity
Open this publication in new window or tab >>Ultracold atoms in optical potentials: from noise-induced transport to superfluidity
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis, both experimental studies and numerical simulations of ultracold atoms in optical potentials are presented in a collection of nine scientific papers. In particular, noise-induced transport in dissipative optical lattices and superfluid properties of Bose-Einstein condensates have been studied.

Noise is usually regarded as a complication to most systems and as something that needs to be minimized. However, in a series of experiments at Umeå University, noise has been shown to play a key role for laser-cooled cesium atoms trapped in dissipative optical lattices. By using a combination of two dissipative optical lattices, where the relative spatial phase between them can be controlled, a so-called Brownian motor can be realized, where energy can be extracted from the inherent noise. In the experiment, this energy is used to control the transport of the laser-cooled atoms in real time and along pre-designed paths. This thesis also presents a way to characterize this system in terms of energy conversion efficiency and coherence of the transport, which may allow for a more straightforward comparison with other systems that rely on noise rectification. In the studies, it is also shown that the noise triggers a downward drift due to gravity, even though the optical potential should support the atoms. Further investigation of this might help to understand the underlying principles of laser cooling, as well as showing that the system might be suitable as a flexible test bed for statistical physics. In close relation to the experimental system, two numerical simulations are also presented, one in which different ways to induce asymmetries between two periodic potentials are investigated, and one in which a proposal for detecting quantum walks is explored.

In the second part of the thesis, a work from the Joint Quantum Institute is presented, where a long-lived persistent current in a toroidal Bose-Einstein condensate, held in an all-optical trap, is created. The critical velocity of the superflow is measured in the presence of a tunable barrier. The system can be seen as a first realization of an elementary closed-loop atom circuit. Finally a theoretical study of the crossover between one- and two-dimensional systems is presented, in particular the transition between a two-dimensional superfluid to a one-dimensional Mott insulator is investigated.

Abstract [sv]

Medelst nio vetenskapliga artiklar presenteras i denna avhandling experimentella och teoretiska studier av ultrakalla atomer fångade i optiska potentialer. Framförallt har brusinducerade transporter och supraytande egenskaper hos Bose-Einstein-kondensat studerats.

    För de flesta system betraktas brus som något negativt som bör minimeras, men i en serie experiment som redovisas i denna avhandling spelar bruset istället en avgörande positiv roll. I ett system där laserkylda atomer genom växelverkan med laserstrålar fångas i två individuella optiska kristallgitter, kan atomernas kollektiva rörelse styras genom att energi utvinns ur det inneboende bruset. I denna avhandling, genom att kontrollera de optiska potentialerna i realtid, visas att atomernas kollektiva rörelse kan styras längs förutbestämda banor med en så kallade Brownska motor. I ett annat experiment mäts verkningsgraden i omvandligen mellan brus och arbete, samt koherensen i atomtransporten. En sådan karakterisering gör att systemet blir enklare att jämföra med andra system som bygger på liknande principer. I avhandlingen presenteras också en studie där det visas att det inneboende bruset i systemet, tillsammans med en svag kraft, i detta fall från gravitation, kan skapa drifter trots att de optiska potentialerna borde vara tillräckligt djupa för att atomerna ska vara fångade. Denna upptäckt kan leda till ökad grundläggande kundskap om laserkylning. Dessutom visar det att systemet kan beskrivas med modeller från statistisk fysik. I relation till det experimentella systemet i Umeå redovisas även två teoretiska studier, en för två symmetriska periodiska potentialer och deras sätt att möjliggöra inducerade drifter med olika typ av asymmetrier, samt en annan för möjligheten att genomföra och detektera kvantvandringar.

    I avhandlingen presenteras också ett experimentellt arbete utfört vid Joint Quantum Institute, där en långlivad ihållande ström i ett torusformat Bose-Einstein-kondensat har skapats i en optisk fälla. Den kritiska hastigheten på strömmen har mätts i närvaron av en ställbar optisk barriär. Detta system kan ses som en första realisation av en grundläggande atomkrets. Slutligen presenteras även en teoretisk studie av övergången mellan en- och tvådimensionella system, där fasövergången mellan superytande och Mottisolation studeras.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, Institutionen för fysik, 2011. 72 p.
Keyword
Brownian motors, noise-induced transport, superfluidity, ultracold atoms, optical potentials, optical lattices, laser coooling
Research subject
Physics
Identifiers
urn:nbn:se:umu:diva-39541 (URN)978-91-7459-140-8 (ISBN)
Public defence
2011-02-25, N320, Umeå universitet, Umeå, 16:01 (English)
Opponent
Supervisors
Available from: 2011-02-04 Created: 2011-01-31 Last updated: 2011-05-16Bibliographically approved
2. Atomic transport in optical lattices
Open this publication in new window or tab >>Atomic transport in optical lattices
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis includes both experimental and theoretical investigations of fluctuation-induced transport phenomena, presented in a series of nine papers, by studies of the dynamics of cold atoms in dissipative optical lattices.

With standard laser cooling techniques about 108 cesium atoms are accumulated, cooled to a few μK, and transferred into a dissipative optical lattice. An optical lattice is a periodic light-shift potential, and in dissipative optical lattice the light field is sufficiently close to resonance for incoherent light scattering to be of importance. This provides the system with a diffusive force, but also with a friction through laser cooling mechanisms.

In the dissipative optical lattices the friction and the diffusive force will eventually reach a steady state. At steady state, the thermal energy is low enough, compared to the potential depth, for the atoms to be localized close to the potential minima, but high enough for the atoms to occasionally make inter-well flights. This leads to a Brownian motion of the atoms in the optical lattices. In the normal case these random walks average to zero, leading to a symmetric, isotropic diffusion of the atoms.

If the optical lattices are tilted, the symmetry is broken and the diffusion will be biased. This leads to a fluctuation-induced drift of the atoms. In this thesis an investigation of such drifts, for an optical lattice tilted by the gravitational force, is presented. We show that even though the tilt over a potential period is small compared to the potential depth, it clearly affect the dynamics of the atoms, and despite the complex details of the system it can, to a good approximation, be described by the Langevin equation formalism for a particle in a periodic potential. The linear drifts give evidence of stop-and-go dynamics where the atoms escape the potential wells and travel over one or more wells before being recaptured.

Brownian motors open the possibility of creating fluctuation-induced drifts in the absence of bias forces, if two requirements are fulfilled: the symmetry has to be broken and the system has to be brought out of thermal equilibrium. By utilizing two distinguishable optical lattices, with a relative spatial phase and unequal transfer rates between them, these requirements can be fulfilled. In this thesis, such a Brownian motor is realized, and drifts in arbitrary directions in 3D are demonstrated. We also demonstrate a real-time steering of the transport as well as drifts along pre-designed paths. Moreover, we present measurements and discussions of performance characteristics of the motor, and we show that the required asymmetry can be obtained in multiple ways.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, Institutionen för fysik, 2010. 83 p.
Keyword
Ultra-cold atoms, optical lattice, laser cooling, directed transport, Brownian motor, Brownian motion
Identifiers
urn:nbn:se:umu:diva-38648 (URN)978-91-7459-123-1 (ISBN)
Public defence
2011-01-21, Naturvetarhuset, N200, Umeå universitet, Umeå, 10:00 (English)
Opponent
Supervisors
Available from: 2010-12-21 Created: 2010-12-20 Last updated: 2011-05-16Bibliographically approved

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