Presentation on theme: "Laser Cooling and Trapping of Atom"— Presentation transcript:
1 Laser Cooling and Trapping of Atom Ying-Cheng Chen, 陳應誠Institute of Atomic and Molecular Science, Academic Sinica,中研院原分所
2 Outline Basic idea & concept Overview of laser cooling and cold atom studyThe light forceDoppler cooling for a two-level atomSub-Doppler CoolingOthers cooling schemePractical issues about a Magneto-Optical Trap (MOT)Atomic speciesLasersVacuumMagnetic fieldImaging
3 Temperature LandmarkTo appreciate something is a good motivation to learn something!106103110-310-610-9(K)core of sunsurface of sunroomtemperatureL N2L He3He superfluidity2003 MITNa BECtypical TCof BECMOTsub-DopplercoolingLaser cooling and trapping of atom is a breakthrough to the exploration of theultracold world. A 12 orders of magnitude of exploration toward absolute zero temperature from room temperature !!!
4 What is special in the ultracold world? A bizarre zoo where Quantum Mechanics governsWave nature of matter, interference, tunneling, resonanceQuantum statisticsUncertainty principle, zero-point energySystem must be in an ordered stateQuantum phase transition~1μm for 100nk
6 Useful References Books, Review articles H. J. Metcalf & P. van der Straten, “Laser cooling and trapping”C. J. Pethick & H. Smith ,“Bose-Einstein condensation in dilute gases”P. Meystre, “Atom optics”C. Cohen-Tannoudji, J. Dupont-Roc & G. Grynberg “Atom-Photon interaction”Review articlesV. I. Balykin, V. G. Minogin, and V. S. Letokhov, “Electromagnetic trapping of cold atoms” , Rep. Prog. Phys. 63 No 9 (September 2000)V S Letokhov, M A Ol'shanii and Yu B Ovchinnikov Quantum Semiclass. Opt. 7 No 1 (February 1995) 5-40 “Laser cooling of atoms: a review”
7 The Light Force: Concept absorptionemissionAn exchange of momentum &energy between photon and atom !Photon posses energyand momentum !Net moentum exchangefrom the photon to atomForce on atom
8 Energy and Momentum Exchange between Atom and Photon Photon posses momentum and energy.Atom absorbs a photon and re-emit another photon.always positive, recoil heatingCriteria of laser coolingIf the momentum decrease, and ifthe kinetic energy decrease,where avg stands for averaging over photon scattering events.A laser cooling scheme is thus an arrangement of an atom-photointeraction scheme that satisfy the above criteria!
9 The Light force : quantum mechanics Ehrenfest theorem, the quantum-mechanical analogue of Newton’s second law,where V(r,t) is the interaction potential.Interaction potential: for an atom interacting with the laser field, , where d is atomic dipole moment operator.Semi-classical treatment of atomic dynamics:Atomic motion is described by the averaged velocityEM field is treat as a classical fieldAtomic internal state can be described by a density matrix which is determined by the optical Bloch equation
10 Validity of semi-classical treatment Momentum width p is large compared with photon momentum k.Atom travel over a distance smaller than the optical wavelength during internal relaxation time. (Internal variables are fast components and variation of atomic motion is slow components in density matrix of atom ρ(r,v,t))Two conditions are compatible only ifIf the above conditions is not fullified, full quantum-mechanical treatment is needed. e.g. Sr narrow-line cooling, =27.5kHz ~ ωr=2k/2m=24.7kHzan upper bound on van lower bound on vorJ. Dalibard & C. Cohen-Tannoudhi, J. Phys. B. 18,1661,1985T.H. Loftus et.al. PRL 93, ,2004
11 The light force for a two-level atom Where d12=d21 are assumed to be real and we have introduced the Bloch vectors u,v, and w.Remark: dipole moment containin phase and in quadraturecomponents with incident field.ρij (or σij)can be determined by the optical Bloch equation of atomic density matrix.
12 Optical Bloch equation Incoherent part due to spontaneousemission or others relaxation processessteady state solutionIsat ~ 1-10 mW/cm2 for alkali atom
13 Two types of forces Without loss of generality, choose At r =0, Take average over one optical cycledipole force orgradient forcea reactive forceradiation pressure orspontaneous emission forcea dissipative forceOrigin of optical trappingOrigin of optical cooling
15 Spontaneous emission force Fromfor steady-stateDecay rate,For a plane wave,where Rsp is the flourescence rate.Max deceleration for Na D2 line !
16 Dipole Force in a standing wave A standing wave has an amplitude gradient, but not a phase gradient. So only the dipole force exists.Where s0 is the saturation parameter for each of the two beams that form the standing wave.For δ<0 (red detuning), the force attracts atom toward high intensity regions.For δ>0 (blue detuning), the force repels atom away from high intensity regions.
17 Velocity dependent force Atom with velocity v experiences a Doppler shift kv.The velocity range of the force is significant for atoms with velocity such that their Dopplerdetunings keeps them within one linewidth considering the power broadening factor.
18 Doppler Cooling For δ<0, the force slows down the velocity. δ/ [/k]
19 Doppler Cooling limitDoppler cooling : cooling mechanism; Recoil heating : heating mechanismTemperature limit is determined by the relation that cooling rate is equal to heating rate.Recoil heating can be treat as a random walk with momentum step size k.Minimum temperatureTD ~ K for alkali atomFor low intensity s0<<1
21 SubDoppler coolingMany cooling schemes allow one to cool atoms below the Doppler limit, or even down to the recoil limit.Polarization gradient cooling (Sisyphus cooling)Raman coolingVelocity-selective-coherent-population-trapping(VSCPT)cooling…But we won’t discuss in this course.
22 Part II: Practical Issues about a magneto-optical trap
24 Atomic species Different atomic species has its unique feature ! (5s5p)1P132MHz2 3P21.6MHz6 2P3/25.2MHzF=543(5s5p)3P14.7kHz1083nm2cooling2 3S1metastable460.73nmBroad-linecooling689.26nmNarrow-linecooling852.35nmrepumping~20eVby discharge436 2S1/2(5s2)1S01 0S1133Cs, alkali metal, I=7/288Sr, alkali earth, I=04He, nobel gas, I=0
25 LasersDiode lasers are extensive use in laser cooling community due to inexpensive cost and frequency tunability.Diode lasers in external cavity configuration are used to reduce the laser linewidth.Master oscillator power amplifier (MOPA) configuration is used to increase the available laser power.ECDL in Littrow configurationmasterDiode laserECDL in Littman-Metcalf configurationTamperedamplifiierMOPA
26 Laser frequency stabilization Frequency-modulated saturation spectroscopy is the standard setup to generate the error signal for frequency stabilization.Feedback circuits are usually built to lock the laser frequency.laserBackground subtracted saturation spectrometerspectrometerError signalFeedbackcircuit
27 VacuumTwo different kinds of vacuum setup are mainly used, one is glass vapor cell, the other is stainless chamber.Ion pump and titanium sublimation pump are standard setup to achieve ultrahigh vacuum.Vapor-cell MOTChamber MOT
28 Magnetic field Anti-Helmholtz coils for the MOT Magnetic field reach maximum if the distance between two coils equal to the radius of the coilArial field gradient is twice the radial field gradient.Helmholtz coils for earth-compensationMagnetic field is most uniform ~ x4 when the distance between two coils equal to the radius of the coilEarth compensation is critical to get good polarization gradient cooling.The magnitude of magnetic field scales ~ for different atomic species.
29 Imaging Itransmitted(x,y) I0(x,y) z CCD camera From experiment From theoryConsidering the dark count of CCD3* = 0~3, depends on laser polarization andpopulation distribution around Zeeman sublevels
30 How to determine the temperature? t=200 mst=500 mst=1000 mst=2100 msMOT laser200400600800100012001400160018001.681.71.721.741.761.781.81.821.841.861.88x 10-3delay (us)Sigma X (m)datafitMagnetic fieldtImage beam