Cold atoms

                                             Lecture 1.

                                         20. September 2006

                                      Low temperature physics
                              (borrowed from an undergraduate course)

                                      Existence absolutní nuly

                                         Teploty ve vesmíru

                                         Teploty ve vesmíru

                           Nízké  teploty  v  laboratoři   (jen výběr !!)

                                          Naše hlavní téma

                           Nízké  teploty  v  laboratoři   (jen výběr !!)

                            Chlazení jadernou adiabatickou demagnetisací

                        Kryostat, kde byla dosažena rekordní teplota  100 pK

                       Spinová magnetická susceptibilita monokrystalu rhodia



                                   Introductory matter on bosons

                               Bosons and Fermions (capsule reminder)

                               Bosons and Fermions (capsule reminder)

                               Bosons and Fermions (capsule reminder)

                               Bosons and Fermions (capsule reminder)

                               Bosons and Fermions (capsule reminder)

                               Bosons and Fermions (capsule reminder)

                               Bosons and Fermions (capsule reminder)

                               Bosons and Fermions (capsule reminder)

                               Bosons and Fermions (capsule reminder)

                               Bosons and Fermions (capsule reminder)

                               Bosons and Fermions (capsule reminder)

                               Bosons and Fermions (capsule reminder)

                               Bosons and Fermions (capsule reminder)

                                         Examples of bosons

                            Examples of bosons (extension of the table)

      Digression: How a complex particle, like an atom, can behave as a single whole, a boson

      Digression: How a complex particle, like an atom, can behave as a single whole, a boson

      Digression: How a complex particle, like an atom, can behave as a single whole, a boson

                                      Plane waves in a cavity

                                         Density of states



                            Ideal quantum gases at a finite temperature

                            Ideal quantum gases at a finite temperature

                            Ideal quantum gases at a finite temperature

                            Ideal quantum gases at a finite temperature

                            The Planck formula for black-body radiation

                                 Equilibrium radiation in a cavity

                                           Planck formula

                                       Stephan-Boltzmann law

                                       Stephan-Boltzmann law

                                       Stephan-Boltzmann law

                                       Stephan-Boltzmann law

                                       Stephan-Boltzmann law

                      Bose-Einstein condensation:         elementary approach

                         Einstein's  manuscript with the derivation of BEC

                                     What is the nature of BEC?

                             A gas with a fixed average number of atoms

                             A gas with a fixed average number of atoms

                             A gas with a fixed average number of atoms

                             A gas with a fixed average number of atoms

                             A gas with a fixed average number of atoms

                             A gas with a fixed average number of atoms

                                      Condensate concentration

                                      Condensate concentration

                                      Condensate concentration

                                      Condensate concentration

                                      Condensate concentration

                              Digression: simple interpretation of T[C

                          ]de Broglie wave length for atoms and molekules

                            Ketterle explains BEC to the King of Sweden

                                      Condensate concentration

                                  Where are the condensate atoms?

                            Where are the condensate atoms? Continuation

                              Where are the condensate atoms? Summary

                                         Closer look at BEC

                                         Closer look at BEC

                                         Closer look at BEC

                                         Closer look at BEC

                                         Closer look at BEC

                                   Off-Diagonal Long Range Order

                                 Analysis on the one-particle level

                                      Coherence in BEC: ODLRO

                                      Coherence in BEC: ODLRO

                                      Coherence in BEC: ODLRO

                                      Coherence in BEC: ODLRO

                                      Coherence in BEC: ODLRO

                                    OPDM for homogeneous systems

                                OPDM for homogeneous systems: ODLRO

                                OPDM for homogeneous systems: ODLRO

                                OPDM for homogeneous systems: ODLRO

                          From OPDM towards the macroscopic wave function

                          From OPDM towards the macroscopic wave function

                          From OPDM towards the macroscopic wave function

                        F.Laloë: Do we really understand Quantum mechanics,
                                      Am.J.Phys.69, 655 (2001)

                                              The end

                                              Problems