Atom-light interaction Light forces Dressed state picture Laser cooling and trapping and application to superfluid hydrodynamics of Bose gases Lecture 1: Light forces H´el`enePerrin Laboratoire de physique des lasers, CNRS-Universit´eParis 13, Sorbonne Paris Cit´e Coherent quantum dynamics H´el`ene Perrin Laser cooling and trapping Atom-light interaction Light forces Dressed state picture Outline of the course Lecture 1: Light forces Lecture 2: Laser cooling and trapping Lecture 3: [tentative] Superfluid hydrodynamics of a Bose gas in a harmonic (or bubble) trap H´el`ene Perrin Laser cooling and trapping Atom-light interaction Light forces Dressed state picture Outline of the course Lecture 1: Light forces Lecture 2: Laser cooling and trapping Lecture 3: [tentative] Superfluid hydrodynamics of a Bose gas in a harmonic (or bubble) trap H´el`ene Perrin Laser cooling and trapping Atom-light interaction Light forces Dressed state picture Introduction A little bit of history First evidence of the mechanical effect of light on a sodium beam in 1933 by Otto Frisch Doppler cooling first suggested in 1975 by H¨ansch(Nobel 2005) and Schawlow (N. 1981) for neutral atoms and independently by Wineland (N. 2012) and Dehmelt (N. 1989) for ions Zeeman slower demonstrated in 1982 by Phillips (N. 1997) and Metcalf First optical molasses in 1985 by Chu (N. 1997) et al. First dipole trap in 1986 by Ashkin (N. 2018) and Chu Explanation of sub-Doppler cooling in 1989 by Dalibard and Cohen-Tannoudji (N. 1997) Sub-recoil laser cooling in the 90's (VSCPT, Raman cooling) Bose-Einstein condensation reached in 1995 by Cornell, Wieman and Ketterle (all N. 2001) H´el`ene Perrin Laser cooling and trapping Atom-light interaction Light forces Dressed state picture Introduction Estimation of the light force Atom irradiated by a resonant laser: plane wave of frequency !, photon momentum ~kL ~kL Each absorption changes the velocity by vrec = M . Spontaneous emissions cancel on average net acceleration along the laser alaser = Γscvrec ) −1 7 −1 Typical numbers: for rubidium, vrec = 6 mm s ; Γsc 2 10 s · ' × 5 −2 4 acceleration of order alaser 10 m s 10 g! ) ' · ' H´el`ene Perrin Laser cooling and trapping Metrology (fountains, optical clocks, cold atom interferometers...) Quantum information and quantum computation New insights in condensed matter physics and quantum simulation: Bloch oscillations, superfluid-insulator transitions, Cooper Sr optical clock pairing, Anderson localization, simulation of (Katorivortex lattice lab) (Ketterle) magnetic systems... quantumbosonic BEC/ memory fermionic (Kimble)BEC-BCS cross-over Atom-light interaction Light forces Dressed state picture Introduction A wide range of applications: High precision spectroscopy (Doppler-free lines) of atoms and molecules credit: Chukman So anti-hydrogen trapping (ALPHA collaboration) H´el`ene Perrin Laser cooling and trapping Quantum information and quantum computation New insights in condensed matter physics and quantum simulation: Bloch oscillations, credit: Chukman So anti-hydrogen trapping superfluid-insulator transitions, Cooper (ALPHA collaboration) pairing, Anderson localization, simulation of vortex lattice (Ketterle) magnetic systems... quantumbosonic BEC/ memory fermionic (Kimble)BEC-BCS cross-over Atom-light interaction Light forces Dressed state picture Introduction A wide range of applications: High precision spectroscopy (Doppler-free lines) of atoms and molecules Metrology (fountains, optical clocks, cold atom interferometers...) Sr optical clock (Katori lab) H´el`ene Perrin Laser cooling and trapping New insights in condensed matter physics and quantum simulation: Bloch oscillations, credit: Chukman So anti-hydrogen trapping superfluid-insulator transitions, Cooper Sr optical clock (ALPHA collaboration) pairing, Anderson localization, simulation of (Katorivortex lattice lab) (Ketterle) magnetic systems... bosonic BEC/ fermionic BEC-BCS cross-over Atom-light interaction Light forces Dressed state picture Introduction A wide range of applications: High precision spectroscopy (Doppler-free lines) of atoms and molecules Metrology (fountains, optical clocks, cold atom interferometers...) Quantum information and quantum computation quantum memory (Kimble) H´el`ene Perrin Laser cooling and trapping credit: Chukman So anti-hydrogen trapping Sr optical clock (ALPHA collaboration) (Katori lab) quantum memory (Kimble) Atom-light interaction Light forces Dressed state picture Introduction A wide range of applications: High precision spectroscopy (Doppler-free lines) of atoms and molecules Metrology (fountains, optical clocks, cold atom interferometers...) Quantum information and quantum computation New insights in condensed matter physics and quantum simulation: Bloch oscillations, superfluid-insulator transitions, Cooper pairing, Anderson localization, simulation of vortex lattice (Ketterle) magnetic systems... bosonic BEC/ fermionic BEC-BCS cross-over H´el`ene Perrin Laser cooling and trapping Atom-light interaction Light forces Dressed state picture References Lecture notes of this course + an easy EPJST introductive paper + a short bibliography to be found on my personal page http://www-lpl.univ-paris13.fr/bec/BEC/Team_Helene.htm General references { C. Cohen-Tannoudji and D. Gu´ery-Odelin: Advances in atomic physics: an overview (World Scientific, 2011) { C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg: Atom-Photon Interactions : Basic Processes and applications (Wiley, 1992). On laser cooling and trapping: { H. J. Metcalf and P. van der Straten: Laser Cooling and Trapping (Springer, New York, 1999); Atoms and molecules interacting with light (Cambrige UP 2016) { C. Cohen-Tannoudji: Atomic motion in laser light, in Fundamental systems in Quantum optics, Les Houches, Session LIII (Elsevier, 1992). On dipole traps: { R. Grimm, M. Weidem¨ullerand Y. Ovchinnokov: Optical dipole traps for neutral atoms, Adv. At. Mol. Opt. Phys., 42:95{170, 2000. http://arxiv.org/abs/physics/9902072 H´el`ene Perrin Laser cooling and trapping Atom-light interaction Light forces Dressed state picture Outline Outline of the lecture 1 Atom-light interaction Two-level model Dipolar interaction Hamiltonians 2 Light forces Definition of the mean light force Orders of magnitude. Approximations Calculation of the mean force Interpretation of the mean force and applications 3 The dressed state picture System under consideration Eigenstates for the coupled system: the dressed states Spontaneous emission Dipole force H´el`enePerrin Laser cooling and trapping Atom-light interaction Light forces Dressed state picture 2-level Coupling H^ Two-level model The atom has many electronic transitions of frequencies !i . The laser frequency ! is close to one particular frequency !0: detuning ~!i δ = ! !0 such that e Γ − δ !0; !; !i ! for all i = 0. j j j − j 6 ~! ~!0 We can restrict the discussion to these two levels g and e: transition frequency g !0, or wavelength λ0 = 2πc=!0, lifetime of the excited state Γ−1. N.B.: Not valid for a very far off resonant laser [Grimm2000]. H´el`ene Perrin Laser cooling and trapping Atom-light interaction Light forces Dressed state picture 2-level Coupling H^ Dipolar interaction Assume that the wavelength λ0 is in the visible or near IR range. The strongest coupling for a L L + 1 (typically S P) transition is the dipolar electric! coupling V^ = D^ E^!. − · Dipolar coupling D^ = d e g + d∗ g e ; (1) j ih j j ih j where d is the reduced dipole: d = e D^ g d∗ = g D^ e h j j i h j j i We stay in the dipolar approximation for the rest of the lecture. H´el`ene Perrin Laser cooling and trapping Atom-light interaction Light forces Dressed state picture 2-level Coupling H^ Laser electric field The laser field contains many photons, average number N¯. Poissonian number fluctuations ∆N = pN¯ N¯. A classical field describes the laser properly: ) 1 −i!t −iφ(r) EL(r; t) = L(r) L(r) e e + c:c: (2) 2E n o The classical laser amplitude L, polarisation L and phase φ may depend on the position rE. All the quantum fluctuations are set apart (quantum field). H´el`ene Perrin Laser cooling and trapping Atom-light interaction Light forces Dressed state picture 2-level Coupling H^ Three coupled systems Laser, atom and quantum field ΩΓ ~! ~!0 EL V^AL H^A V^AR H^R The total Hamiltonian reads H^ = H^A + H^R + V^AL + V^AR : H´el`ene Perrin Laser cooling and trapping Atom-light interaction Light forces Dressed state picture 2-level Coupling H^ Hamiltonians Atom: position R^, momentum P^ ^ 2 ^ P HA = ~!0 e e + : (3) j ih j 2M Quantum field: If the quantum modes of the field are labelled by ` = (k; ), the energy of the quantum modes is given by ^ y HR = ~!` a^`a^` : ` X For the description of the atom motion, we will trace on the quantum field variables. Atom to quantum field coupling: V^AR is responsible for spontaneous emission and for the coupling to the laser field fluctuations. It is not necessary to give an explicit form of this term here. H´el`ene Perrin Laser cooling and trapping Atom-light interaction Light forces Dressed state picture 2-level Coupling H^ Hamiltonians Atom-laser coupling: res non res V^AL = D^ EL(R^; t) = V^ + V^ − · AL AL res 1 −i!t −iφ(R^) V^ = d (R)^ L(R^) e g e e + h:c: AL −2 · E j ih j 1 h i ^ V^non res = d ∗(R)^ ∗(R^) e g ei!t eiφ(R) + h:c: AL −2 · EL j ih j h i In the Heisenberg picture, e g evolves as ei!0t ^res j ih j VAL describes a slow evolution (at frequency δ = ! !0) while )^non res − VAL describes a fast evolution (at frequency ! + !0). H´el`ene Perrin Laser cooling and trapping Atom-light interaction Light forces Dressed state picture 2-level Coupling H^ Hamiltonians We introduce the Rabi frequencyΩ 1(r) defined by ~Ω1(r) = [d (r)] L(r) : (4) − · E The time origin is chosen such that Ω1 is real. The atom-laser resonant coupling can then be written as ^ res ~Ω1(R) −i!t −iφ(R^) V^ = e g e e + h:c: (5) AL 2 j ih j n o The Rabi frequency is the oscillation frequency between g and e at resonance in the strong coupling regime.