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Atomic transport in optical lattices
Umeå University, Faculty of Science and Technology, Department of Physics.
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 [en]
Ultra-cold atoms, optical lattice, laser cooling, directed transport, Brownian motor, Brownian motion
Identifiers
URN: urn:nbn:se:umu:diva-38648ISBN: 978-91-7459-123-1 (print)OAI: oai:DiVA.org:umu-38648DiVA: diva2:379807
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
List of papers
1. Directed transport with real-time external steering and drifts along pre-designed paths using a Brownian motor
Open this publication in new window or tab >>Directed transport with real-time external steering and drifts along pre-designed paths using a Brownian motor
2011 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 83, no 2Article in journal (Refereed) Published
Abstract [en]

We have realized real-time steering of the directed transport in a Brownian motor based on cold atoms in optical lattices and demonstrate drifts along predesigned paths. The transport is induced by spatiotemporal asymmetries in the system, where we can control the spatial part, and we show that the response to changes in asymmetry is very fast. In addition to directional steering, a real-time control of the magnitude of the average drift velocity and an on-off switching of the motor are also demonstrated. We use a noninvasive real-time detection of the transport, enabling feedback control of the system.

Identifiers
urn:nbn:se:umu:diva-38521 (URN)10.1103/PhysRevE.83.020101 (DOI)
Note
Received 26 September 2010; published 2 February 2011Available from: 2010-12-16 Created: 2010-12-16 Last updated: 2017-12-11Bibliographically approved
2. Breaking the symmetry of a Brownian motor with symmetric potentials
Open this publication in new window or tab >>Breaking the symmetry of a Brownian motor with symmetric potentials
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
National Category
Other Physics Topics
Research subject
Physics
Identifiers
urn:nbn:se:umu:diva-42554 (URN)10.1088/1751-8113/44/15/155002 (DOI)
Available from: 2011-04-14 Created: 2011-04-08 Last updated: 2011-05-16Bibliographically approved
3. Experimental measurement of the efficiency and the transport coherence of a cold-atom Brownian motor realized with cold atoms in optical lattices
Open this publication in new window or tab >>Experimental measurement of the efficiency and the transport coherence of a cold-atom Brownian motor realized with cold atoms in optical lattices
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2011 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 83, no 2, 020102Article in journal (Refereed) Published
Abstract [en]

The rectification of noise into directed movement or useful energy is utilized by many different systems. The peculiar nature of the energy source and conceptual differences between such Brownian motor systems makes a characterization of the performance far from straightforward. In this work, where the Brownian motor consists of atoms interacting with dissipative optical lattices, we adopt existing theory and present experimental measurements for both the efficiency and the transport coherence. We achieve up to 0.3% for the efficiency and 0.01 for the Péclet number.

Place, publisher, year, edition, pages
American Physical Society, 2011
National Category
Physical Sciences
Identifiers
urn:nbn:se:umu:diva-38520 (URN)10.1103/PhysRevE.83.020102 (DOI)
Note

Received 16 September 2010; published 3 February 2011

Available from: 2010-12-16 Created: 2010-12-16 Last updated: 2017-12-11
4. Fluctuation-induced drift in a gravitationally tilted optical lattice
Open this publication in new window or tab >>Fluctuation-induced drift in a gravitationally tilted optical lattice
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2010 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 82, no 3, 031136- p.Article in journal (Refereed) Published
Abstract [en]

Experimental and theoretical studies are made of Brownian particles trapped in a periodic potential, which is very slightly tilted due to gravity. In the presence of fluctuations, these will trigger a measurable average drift along the direction of the tilt. The magnitude of the drift varies with the ratio between the bias force and the trapping potential. This can be closely compared to a theoretical model system, based on a Fokker-Planck equation formalism. We show that the level of control and measurement precision we have in our system, which is based on cold atoms trapped in a three-dimensional dissipative optical lattice, makes the experimental setup suitable as a testbed for fundamental statistical physics. We simulate the system with a very simplified and general classical model, as well as with an elaborate semiclassical Monte Carlo simulation. In both cases, we achieve good qualitative agreement with experimental data.

National Category
Other Physics Topics
Research subject
Physics
Identifiers
urn:nbn:se:umu:diva-36914 (URN)10.1103/PhysRevE.82.031136 (DOI)000282134100005 ()
Available from: 2010-10-21 Created: 2010-10-13 Last updated: 2017-12-12Bibliographically approved
5. Theoretical investigation of quantum walks by cold atoms in a double optical lattice
Open this publication in new window or tab >>Theoretical investigation of quantum walks by cold atoms in a double optical lattice
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2009 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 80, no 1, 012302- p.Article in journal (Refereed) Published
Abstract [en]

We investigate the feasibility of carrying out quantum walks with cold atoms in a double optical lattice. Monte Carlo simulations of time-of-flight (TOF) detection and absorption imaging were carried out, focusing on a specific experimental implementation. These indicate that absorption imaging would be best suited for detection of quantum walks. With typical experimental parameters a few hundred quantum walk steps will be needed for an unambiguous detection of the quantum walk signature. We show that in special cases, few-step quantum walks can also be detected in our system if one measures the relative population of the atoms in their internal states rather than their displacement in space, that is, measurements are made in the space of the coin operator rather than in that of the displacement operator.

Place, publisher, year, edition, pages
American Physical Society, 2009
Identifiers
urn:nbn:se:umu:diva-38522 (URN)10.1103/PhysRevA.80.012302 (DOI)
Available from: 2010-12-16 Created: 2010-12-16 Last updated: 2017-12-11Bibliographically approved
6. Assessment of a time-of-flight detection technique for measuring small velocities of cold atoms
Open this publication in new window or tab >>Assessment of a time-of-flight detection technique for measuring small velocities of cold atoms
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2009 (English)In: Journal of Applied Physics, ISSN 0021-8979, E-ISSN 1089-7550, Vol. 105, no 8, 083109- p.Article in journal (Refereed) Published
Abstract [en]

A low noise time-of-flight detection system for laser cooled atoms has been constructed and incrementally optimized. Here, a thorough description of the construction is presented along with an analysis of the capabilities of the system. The quality of the detection (the resolution, the reproducibility, the sensitivity, etc.) is crucial for, e.g., the ability to see details in the velocity distribution profile, which is of interest for fundamental studies of statistical physics and of the laser cooling processes, and for detection of small initial velocities of an atomic cloud, important, e.g., when studying small drifts induced by Brownian motors and ratchets. We estimate the signal-to-noise ratio of our signal to be better than 1000:1 for a typical single shot, and we discuss the effect of the initial atomic cloud size, the probe size, and the effects of the wave packet spread during the fall time on the measured quantities. We show that the shape of the velocity distribution is well conserved during the mapping done in the detection, i.e., in the convolution with the probe beam, and that velocities as small as a few percent of the single photon recoil velocity can be resolved.

National Category
Physical Sciences
Identifiers
urn:nbn:se:umu:diva-38517 (URN)10.1063/1.3097466 (DOI)
Available from: 2010-12-16 Created: 2010-12-16 Last updated: 2017-12-11Bibliographically approved
7. A three-dimensional Brownian motor, realised with symmetric optical lattices
Open this publication in new window or tab >>A three-dimensional Brownian motor, realised with symmetric optical lattices
2009 (English)In: Physica status solidi. B, Basic research, ISSN 0370-1972, E-ISSN 1521-3951, Vol. 246, no 5, 999-1005 p.Article in journal (Refereed) Published
Abstract [en]

A three-dimensional Brownian motor is realised using lasercooled caesium atoms trapped in a system of two static, and individually symmetric, optical lattices; a so-called double optical lattice. Isotropic fluctuations, emanating from light scattering, are rectified, and the diffusion of the ensemble of atoms is biased, with a resulting constant velocity that is controllable both in direction and magnitude. The working principle of the Brownian motor can be seen as a pulsation between two different potentials, both symmetric but around different points. The correlation between interferometric spatial offsets, and imbalance in optical pumping rates, leads to a spatio-temporal asymmetry sufficient for generating a controlled, directed motion.

National Category
Atom and Molecular Physics and Optics
Research subject
Physics
Identifiers
urn:nbn:se:umu:diva-30839 (URN)10.1002/pssb.200881559 (DOI)
Available from: 2010-01-19 Created: 2010-01-19 Last updated: 2017-12-12Bibliographically approved
8. Influence of the lattice topography on a three-dimensional, controllable Brownian motor
Open this publication in new window or tab >>Influence of the lattice topography on a three-dimensional, controllable Brownian motor
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2008 (English)In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 81, no 3, 33001- p.Article in journal (Refereed) Published
Abstract [en]

We study the influence of the lattice topography and the coupling between motion in different directions, for a three-dimensional Brownian motor based on cold atoms in a double optical lattice. Due to controllable relative spatial phases between the lattices, our Brownian motor can induce drifts in arbitrary directions. Since the lattices couple the different directions, the relation between the phase shifts and the directionality of the induced drift is non-trivial. Here is therefore this relation investigated experimentally by systematically varying the relative spatial phase in two dimensions, while monitoring the vertically induced drift and the temperature. A relative spatial phase range of 2pi x 2pi is covered. We show that a drift, controllable both in speed and direction, can be achieved, by varying the phase both parallel and perpendicular to the direction of the measured induced drift. The experimental results are qualitatively reproduced by numerical simulations of a simplified, classical model of the system.

National Category
Atom and Molecular Physics and Optics Other Physics Topics
Identifiers
urn:nbn:se:umu:diva-8458 (URN)10.1209/0295-5075/81/33001 (DOI)
Available from: 2008-11-07 Created: 2008-11-07 Last updated: 2017-12-14Bibliographically approved
9. Characterisation of a three-dimensional Brownian motor in optical lattices
Open this publication in new window or tab >>Characterisation of a three-dimensional Brownian motor in optical lattices
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2007 (English)In: European Physical Journal D: Atomic, Molecular and Optical Physics, ISSN 1434-6060, E-ISSN 1434-6079, Vol. 44, no 2, 381-388 p.Article in journal (Refereed) Published
Abstract [en]

We present here a detailed study of the behaviour of a three dimensional Brownian motor based on cold atoms in a double optical lattice [P. Sjölund et al., Phys. Rev. Lett. 96, 190602 (2006)]. This includes both experiments and numerical simulations of a Brownian particle. The potentials used are spatially and temporally symmetric, but combined spatiotemporal symmetry is broken by phase shifts and asymmetric transfer rates between potentials. The diffusion of atoms in the optical lattices is rectified and controlled both in direction and speed along three dimensions. We explore a large range of experimental parameters, where irradiances and detunings of the optical lattice lights are varied within the dissipative regime. Induced drift velocities in the order of one atomic recoil velocity have been achieved.

Place, publisher, year, edition, pages
Springer Verlag, 2007
National Category
Atom and Molecular Physics and Optics
Research subject
Physics
Identifiers
urn:nbn:se:umu:diva-16377 (URN)10.1140/epjd/e2007-00233-3 (DOI)
Available from: 2010-03-08 Created: 2007-09-18 Last updated: 2017-12-14Bibliographically approved

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