Theory of boseeinstein condensation in trapped gases. The discovery of boseeinstein condensation mathematical description of bose einstein condensates experimental results boseeinstein condensation lukassebeke university of stuttgart. Boseeinstein condensation represents a new state of matter and is one of the cornerstones of quantum physics, resulting in the 2001 nobel prize. Ultracold atomic gases is a rapidly developing area of physics that attracts many young researchers around the world. Boseeinstein condensation of photons in an optical microcavity. Various theoretical approaches to describing the physics of interacting bosons and of interacting fermi gases, giving rise to. In this lecture some basic concepts of bose einstein condensation bec were discussed. In 1925 einstein predicted that at low temperatures particles in a gas could all reside in the same quantum state. We consider the case of spinless bosons so there is no spin factor in the density of states of section 4. This book is an introductory text to the physics of boseeinstein condensation.
Bose einstein condensates confined in traps exhibit unique features which have been the object of extensive experimental and theoretical studies in the last few years. Shock waves in quasi onedimensional boseeinstein condensate. Since the experimental demonstration of bose einstein condensation in dilute atomic gases there has been an explosion of interest in the properties of this novel macroscopic quantum system. Boseeinstein condensation in dilute gases will be useful to newcomers to the field and will help researchers with diverse backgrounds communicate with each other. Boseeinsteincondensation letn n c v l3 c g 32z ebe 0n l 3 c 2. A diffusive behaviour of the goldstone mode is found in the spatially homogeneous case and new features are. Boseeinstein condensation by pitaevskii and coauthor sandro stringari, who is another major contributor to the recent theoretical literature, reflects the brief history just sketched. In a fermi gas, bose einstein condensation of pairs was measured by ramping the scattering length to the bec side and detecting the resulting bimodal distribution condensation of pairs measured at unitarity 1a0 as a function of temperature. A new boseeinstein condensate created at aalto university duration. Theory of boseeinstein condensation in trapped gases arxiv. Bose einstein condensation bec is a mechanism for producing a macroscopic quantum system, and is exemplary of the macroscopic quantum phenomena of superconductivity and superfluidity. Josephson junction arrays provide a physical realization of this mechanism. We study analytically and numerically the generation of shock waves in a quasionedimensional boseeinstein condensate bec made of dilute and ultracold alkalimetal atoms. Numerical solution of the grosspitaevskii equation for.
Bose einstein condensation bose einstein condensation in atomic gases. Stringari this book is an introductory text to the physics of bose einstein condensation. Conclusions i below a critical temperature t c bose einstein condensation takes place. Roomtemperature boseeinstein condensation of cavity. This phenomenon, first predicted by einstein in 1925 has been realized experimentally in 1995 in a remarkable series of experiments whose importance has been recognized. Nov 24, 2010 boseeinstein condensation has been observed in several physical systems, but is not predicted to occur for blackbody radiation such as photons. This volume introduces the basic concepts of boseeinstein condensation and superfluidity. Cambridge core condensed matter physics, nanoscience and mesoscopic physics universal themes of bose einstein condensation edited by nick p. Complete boseeinstein condensation in the grosspitaevskii. The condensate is actually a new state of matter, where quantummechanical wave functions of. Measurements of the coherent atomic current in an array of josephson junctions and the.
Although first proposed by einstein in 1924, boseeinstein condensation bec in a gas was not achieved until 1995 when, using a combination of laser cooling. This is the first book devoted to boseeinstein condensation bec as an interdisciplinary subject, covering atomic and molecular physics, laser physics, low temperature physics and astrophysics. The aim of the infmcnr research and development center on boseeinstein condensation bec is to promote theoretical research on the various phenomena related to boseeinstein condensation and to the physics of cold atomic gases in traps. Assuming the unscaled potential to be sufficiently weak, we prove complete boseeinstein condensation for the ground state and for manybody states with finite excitation energy in the limit of large n with a uniform.
A strong boost to the investigation of boseeinstein condensates was. Gross pitaevskii equation for the order parameter and beyond cnrinfm. Bose einstein condensates of excitonpolaritons have been stabilized in a range of crystalline systems. He has developed in a systematic way the sum rule approach to the collective behavior of interacting systems. Exact theory for t0 weakly interacting bose gases follows from schrodinger equation. Under such conditions, a large fraction of bosons occupy the lowest quantum state, at which point microscopic quantum phenomena, particularly wavefunction interference. This phenomenon, first predicted by einstein in 1925 has been. Nls equation has been studied for decades in the various fields of nonlinear optics 66, bose einstein condensation 93 or fluid dynamics 68. This book is an introductory text to the physics of bose einstein condensation. The former work considers the case of simple integrator sde dynamics for a particular class of mfgs, which shows strong analogies with the nonlinear schrodinger and explicitly treating the grosspitaevskii equation. The book is an introductory text to the physics of bose einstein condensation. Bose einstein condensation is a fundamental phenomenon of nature. We consider an interacting, dilute bose gas trapped in a harmonic potential at a positive temperature. Fermi, varenna, july 2008 polariton boseeinstein condensation.
He has developed in a systematic way the sum rule approach to. Written by world renowned experts in the field, this book gives a comprehensive overview of exciting developments in boseeinstein condensation and superfluidity from a. Bose einstein condensation definition, a phase of matter in which all bosons in a given physical system have been cooled to a temperature near absolute zero and enter the same quantum state. Boseeinstein condensation in inhomogeneous josephson arrays. Universal themes of boseeinstein condensation edited by nick. A theoretical overview institute of theoretical physics. The spectrum of elementary excitations around the stationary state is analytically studied in different geometries.
In preparation for the numerics we scale the 3d grosspitaevskii equation and obtain a fourparameter model. Series of monographs on physics oxford university press 2003. Only 50% of pairs are bose einstein condensed at zero temperature strongly interacting gas. Written by world renowned experts in the field, this book gives a comprehensive overview of exciting developments in bose einstein condensation and superfluidity from a theoretical perspective. Boseeinstein condensation in this section we discuss the thermodynamic properties of the ideal bose gas. Boseeinstein condensation and superfluidity key concepts in low temperature physics. Einstein 192425 extended bose s idea to material particles predicted bec in an ideal quantum gas i w.
I a mean eld approach leads to the gross pitaevskii equation which has to be ful lled by the singleparticle wave functions in order to minimize the total energy in the system. Bose einstein condensation represents a new state of matter and is one of the cornerstones of quantum physics, resulting in the 2001 nobel prize. Sandro stringari is an italian theoretical physicist, who has contributed to the theory of quantum manybody physics, including atomic nuclei, quantum liquids and ultracold atomic bose and fermi gases. Excitations in a nonequilibrium boseeinstein condensate. Boseeinstein condensation and superfluidity oxford. Providing a useful introduction to one of the most exciting field of physics today, this text will be of interest. Boseeinstein condensation and superfluidity international. This phenomenon, first predicted by einstein in 1925 has been realized experimentally in 1995 in a remarkable series of experiments whose importance has been recognized by the award of the 2001 nobel prize in physics. Jump to content jump to main navigation jump to main navigation. Here, we created bose polarons near quantum criticality by immersing atomic impurities in a bose einstein condensate bec with nearresonant interactions.
It is an excellent text, a broad survey with some indepth discussions an excellent text such as this is. Lev pitaevskii, senior researcher, university of trento,sandro stringari, professor of theoretical physics, university of trento lev p. Boseeinstein condensation in dilute gases in 1925 einstein. Download pdf bose einstein condensation free online. Bose einstein condensation of 7li has been studied in a magnetically trapped gas. This gaseous state, a bose einstein condensate, was produced in the laboratory for the first time in 1995 and investigating such condensates is one of the most active areas in contemporary physics. This is the first book devoted to bose einstein condensation bec as an interdisciplinary subject, covering atomic and molecular physics, laser physics, low temperature physics and astrophysics.
Some of the assumptions of the gross pitaevskii equation gpe are. Boseeinstein condensation of exciton polaritons nature. Aauniversity of illinois at urbanachampaign, abuniversity of illinois at urbanachampaign, acuniversity of illinois at urbanachampaign publication. Lev pitaevskii and sandro stringari, oxford university press, oxford, 2003. We use cookies for various purposes including analytics. The system is analyzed in a combination of a thermodynamic and a gross pitaevskii gp limit where the trap frequency \\omega\, the temperature t, and the particle number n are related by \n \sim t \omega3 \to\infty\ while the scattering length is so small that the. Boseeinstein condensation in a dilute, trapped gas at. Boseeinstein condensation remains, however, fundamental to the superfluid properties of helium4. This book gives a comprehensive overview of exciting developments in. It makes special reference to the physics of ultracold atomic gases. Boseeinstein condensation and superfluidity ebook, 2016. This volume introduces the basic concepts of bose einstein condensation and superfluidity. Proceedings of the international school of quantum electronics 27th course on bose einstein condensates and atom lasers, october 1924, 1999, erice, italy.
S stringari ultracold atomic gases is a rapidly developing field of physics that attracts many young researchers around the world. Emergent nonlinear phenomena in boseeinstein condensates. We have developed a meanfield model to describe the dynamics of a nonequilibrium bose einstein condensate of excitonpolaritons in a semiconductor microcavity. Bose einstein condensates of dilute gases offer a rich field to study fundamental quantummechanical processes, manipulation of the speed at which light propogates, observation of atomic pair. Nov 20, 2015 boseeinstein condensation vulgarisation. Bose einstein condensates portant, since bec in lower dimensions is not as simple as in 3d. Mathematical theory and numerical methods for boseeinstein. Boseeinstein condensation and superfluidity hardcover. The early experiments on bose einstein condensation in dilute atomic gases accomplished three longstanding goals. Nevertheless, such a mathematical model provides the simplest example for the realization of boseeinstein condensation. The interacting bose gas with repulsive potential is considered in the polymer representation and some of the yet unsolved mathematical questions for establishing the existence of bose condensation in this setting are discussed. Grosspitaevskii equation in boseeinstein condensates. We study the numerical solution of the timedependent grosspitaevskii equation gpe describing a bose einstein condensate bec at zero or very low temperature. Now, polaritons are shown to condense at room temperature using a microcavity within an.
P pitaevskii and s stringari theory of bose einstein condensation. The book is an introductory text to the physics of boseeinstein condensation. The remainder is devoted specifically to the dilute alkali gases. I a mean eld approach leads to the gross pitaevskii equation. Theory and experiment springerverlag berlin heidelberg p. Boseeinstein condensation of atomic gases phys ens.
Sandro stringari at the university of t rento italy. Bose einstein condensation by stringari and pitaevskii. We study certain stationary and timeevolution problems of trapped bose einstein condensates using the numerical solution of the gross pitaevskii equation with. Pitaevskii is a researcher at the cnr trento research center on bose einstein condensation and at the kapitza institute for physical problems in moscow. Bose einstein condensation definition of bose einstein. Recent major progress in atomic quantum gases main object of the present course 2bec can be defined at equilibrium superfluidity mainly related to transport phenomena natural link between bec and superfluidity provided by order parameter. Meanfield theory provides a framework to understand the main features of the condensation and the role of interactions between particles. These include the concept of long range order, the behaviour of the eigenvalues of the 1body density matrix and the concept of order parameter as a classical field. Download pdf bose einstein condensates and atom lasers. Bose einstein condensation in dilute gases will be useful to newcomers to the field and will help researchers with diverse backgrounds communicate with each other. Pdf the theory of boseeinstein condensation of dilute gases. It is an excellent text, a broad survey with some indepth discussions an excellent text such as this is needed in these exciting times.
Theory of ultracold atomic fermi gases stefano giorgini, lev p. Various properties of these systems are discussed, including the density profiles and the energy of the ground state configurations, the. Frantzeskakis, professor ricardo carreterogonzalez eds. Gross pitaevskii equation in boseeinstein condensates. Boseeinstein condensation and superfluidity in trapped.
Using radiofrequency spectroscopy, we probed the energy, spectral width, and shortrange correlations of the impurities as a function of temperature. Sep 28, 2006 boseeinstein condensation bec, a form of matter first postulated in 1924, has famously been demonstrated in dilute atomic gases at ultralow temperatures. Boseeinstein condensation is a phase transition in which a macroscopic number of. Boseeinstein condensation and superfluidity oxford scholarship. These 15 papers provide an introduction to current work on bec. Theory of boseeinstein condensation in trapped gases physical.
Since 1999, a number of other atomic gases have been shown to demonstrate be condensation, including sodium, lithium, and hydrogen. Superfluid helium4 is a liquid rather than a gas, which means that the interactions between the atoms are relatively strong. A good reference is the book bose einstein condensation in dilute gases by pethick and smith. Written by world renowned experts in the field, this book gives a comprehensive overview of exciting. This phenomenon, first predicted by einstein in 1925, has been realized experimentally in 1995 in a remarkable series of experiments whose importance has been recognized by the award of the 2001 nobel prize in physics. Composite structure of vortices in twocomponent bose. Solution to the bose einstein condensation problem gross pitaevskii equations in 3d using fourier transforms. By continuing to use pastebin, you agree to our use of cookies as described in the cookies policy. We show that spatial bose einstein condensation of noninteracting bosons occurs in dimension d 2 over discrete structures with inhomogeneous topology and with no need of external confining potentials. Boseeinstein condensation of an ideal gas an ideal gas consisting of noninteracting bose particles is a.
The experimental realization of bose einstein condensation bec in atomic gases 1 con. A boseeinstein condensate bec is a state of matter also called the fifth state of matter which is typically formed when a gas of bosons at low densities is cooled to temperatures very close to absolute zero 273. Brief bec research history milestones 1924 prediction of bec by a. Boseeinstein condensates in a 1d optical lattice arxiv. Sandro stringari university of trento 1 introduction to bose einstein condensation 3. Wieman 1995 produced the rst gaseous condensate nobel price of physics 2001 about boseeinstein condensation bec history of bec 4 28 c stefan kienzle. Boseeinstein condensation in atomic gases ios press ebooks. It is thought to have played a part in the evolution of the early universe when the particles and forces formed, and the outer layers of a neutron star may well consist of a bec of exotic subatomic particles. Bose einstein condensation and superfluidity international series of monographs on physics series by lev pitaevskii. In this paper i will discuss some issues concerning the behaviour of the order parameter and the dynamic and superfluid effects exhibited by such systems. We introduce measurements of ground state, tunnelling and dynamical properties as well as investigations of atom optical applications and thermodynamical properties. In particular the recent experiments carried out at mit on 23na 2 and at jila on. In this lecture we give an overview on current experiments on bose einstein condensation bec in a onedimensional 1d optical lattice. Linear response theory for gross pitaevskii equation.
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