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The amazing story of Laser Cooling and Trapping following Bill Phillips’ Nobel Lecture http://www.nobelprize.org/nobel_prizes/physics/ laureates/1997/phillips-lecture.pdf Laser cooling of atomic beams 1 Na is not a “two-level” atom! Problem: unwanted optical pumping (a) The optical pumping process preventing cycling transitions in alkalis like Na; (b) (b) use of a repumping laser to allow many absorption-emission cycles. 2 sciencewise.anu.edu.au Another problem: Doppler shift In order for the laser light to be resonantly absorbed by a counterpropagating atom moving with velocity v, the frequency ϖ of the light must be kv lower than the resonant frequency for an atom at rest. As the atom repeatedly absorbs photons, slowing down as desired, the Doppler shift changes and the atom goes out of resonance with the light. The natural linewidth Γ/2π of the optical transition in Na is 10MHz (full width at half maximum). A change in velocity of 6 m/s gives a Doppler shift this large, so after absorbing only 200 photons, the atom is far enough off resonance that the rate of absorption is significantly reduced. The result is that only atoms with the ‘‘proper’’ velocity to be resonant with the laser are slowed, and they are only slowed by a small amount. 3 Cooling an atomic beam with a fixed frequency laser after cooling before cooling The dotted curve is the velocity distribution before cooling, and the solid curve is after cooling. Atoms from a narrow velocity range are transferred to a slightly narrower range centered on a lower velocity. Zeeman slower The laser is tuned so that, given the field induced Zeeman shift and the velocity-induced Doppler shift of the atomic transition frequency, atoms with velocity v0 are resonant with the laser when they reach the point where the field is maximum. Those atoms then absorb light and begin to slow down. As their velocity changes, their Doppler shift changes, but is compensated by the change in Zeeman shift as the atoms move to a point where the field is weaker. At this point, atoms with initial velocities slightly lower than v0 come into resonance and begin to slow down. The process continues with the initially fast atoms decelerating and staying in resonance while initially slower atoms come into resonance and begin to be slowed as they move further down the solenoid. 4 Zeeman Cooling http://es1.ph.man.ac.uk/AJM2/Atomtrapping/Atomtrapping.htm Note: optical pumping problem is avoided By shutting off the cooling laser beam and delaying observation until the slow atoms arrived in the observation region, Prodan, Phillips, and Metcalf (1982) were able to detect atoms as slow as 40 m/s with a spread of 10 m/s, corresponding to a temperature (in the atoms’ rest frame) of 70 mK. The next step was to get these atoms to come to rest in the observation region. 5 Magnetic trapping The idea of magnetic trapping is that in a magnetic field, an atom with a magnetic moment will have quantum states whose magnetic or Zeeman energy increases with increasing field and states whose energy decreases, depending on the orientation of the moment compared to the field. The increasing-energy states, or low-field seekers, can be trapped in a magnetic field configuration having a point where the magnitude of the field is a relative minimum. (a) Spherical quadrupole trap with lines of B-field. (b) Equipotentials of our trap (equal field magnitudes in millitesla), in a plane containing the symmetry (z) axis. Magneto-optical trapping (MOT) 6 Doppler cooling in one dimension Laser beams are tuned slightly below the atomic resonance frequency. An atom moving toward the left sees that the laser beam opposing its motion is Doppler shifted toward the atomic resonance frequency. It sees that the laser beam directed along its motion is Doppler shifted further from its resonance. The atom therefore absorbs more strongly from the laser beam that opposes its motion, and it slows down. The same thing happens to an atom moving to the right, so all atoms are slowed by this arrangement of laser beams. Optical molasses A sodium atom cooled to the Doppler limit has a ‘‘mean free path’’ (the mean distance it moves before its initial velocity is damped out and the atom is moving with a different, random velocity) of only 20 mm, while the size of the laser beams doing the cooling might easily be one centimeter. Thus, the atom undergoes diffusive, Brownianlike motion, and the time for a laser cooled atom to escape from the region where it is being cooled is much longer than the ballistic transit time across that region. This means that an atom is effectively ‘‘stuck’’ in the laser beams that cool it. This stickiness, and the similarity of laser cooling to viscous friction, prompted the Bell Labs group (Chu et al., 1985) to name the intersecting laser beams ‘‘optical molasses.’’ 7 Optical molasses Experimental molasses lifetime (points) and the theoretical decay time (curve) vs detuning of molasses laser from resonance. Doppler cooling limit This cooling process leads to a temperature whose lower limit is on the order of ħΓ, where Γ is the rate of spontaneous emission of the excited state (Γ-1 is the excited state lifetime). The temperature results from an equilibrium between laser cooling and the heating process arising from the random nature of both the absorption and emission of photons. The random addition to the average momentum transfer produces a random walk of the atomic momentum and an increase in the mean square atomic momentum. This heating is countered by the cooling force F opposing atomic motion. 8 Time-of-flight method for measuring laser cooling temperatures The predicted lower limit of Doppler cooling: 240 mK Time-of-flight method for measuring laser cooling temperatures The experimental TOF distribution (points) and the predicted distribution curves for 40 mK and 240 mK (the predicted lower limit of Doppler cooling). Conclusion: atoms were much colder than the Doppler limit! 9 ‘‘Sisyphus’’ cooling The atom is now again at the bottom of a hill, and it again must climb, losing kinetic energy, as it moves. (a) Interfering, counterpropagating beams having orthogonal, linear polarizations create a polarization gradient. (b) The different Zeeman sublevels are shifted differently in light fields with different polarizations; optical pumping tends to put atomic population on the lowest energy level, but nonadiabatic motion results in ‘‘Sisyphus’’ cooling. ‘‘Sisyphus’’ cooling http://www.nobelprize.org/nobel_prizes/physics/laureates/1997/illpres/doppler.html 10 Heterodyne spectrum of fluorescence from Na atoms in optical molasses. The broad component corresponds to a temperature of 84 µK, which compares well with the temperature of 87 µK measured by time-of-flight measurement . The narrow component indicates a sub-wavelength localization of the atoms. Atoms in optical lattices An optical lattice works as follows. When atoms are exposed to a laser field that is not resonant with an atomic optical transition (and thus does not excite the atomic electrons), they experience a conservative potential that is proportional to the laser intensity. With two counterpropagating laser fields, a standing wave is created and the atoms feel a periodic potential. With three such standing waves along three orthogonal spatial directions, one obtains a three-dimensional optical lattice. The atoms are trapped at the minima of the corresponding potential wells. Adapted from: Eugene Demler 11 Sodium laser cooling experiment (1992) WK and Dark SPOT Wolfgang Ketterle, Meridian Lecture Nobel Prize in Physics 1997 Steve Chu Claude Cohen-Tannoudji Bill Phillips 12 fromTheodor W. Hänsch‘s Nobel Lecture Evaporative cooling 13 Quantum gases: bosons and fermions Ideal gas at zero temperature Bose-Einstein Fermi-Dirac EF Bose-Einstein : integer spin Fermi-Dirac : half-integer spin In neutral atoms Nelectrons = Nprotons Salomon et al., ENS Statistical properties are governed by the number of neutrons in an atom Nneutrons : Boson if Nneutrons is even Fermion if Nneutrons is odd Nobel Prize in Physics 2001 Eric Cornell Wolfgang Ketterle Carl Wieman 14 Sodium BEC I experiment (2001) Wolfgang Ketterle, Meridian Lecture Atomic clocks and variation of fundamental constants 15 Clocks 16 Cesium microwave atomic clock 9 192 631 770 periods per second timeandnavigation.si.edu Current definition of a second: 1967: the second has been defined as the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. 1997: the periods would be defined for a cesium atom at rest, and approaching the theoretical temperature of absolute zero (0 K). 17 Cesium atomic clock A gas of cesium atoms enters the clock's vacuum chamber. Six lasers slow the movement of the atoms, cooling them to near absolute zero and force them into a spherical cloud at the intersection of the laser beams. The ball is tossed upward by two lasers through a cavity filled with microwaves. All of the lasers are then turned off. Gravity pulls the ball of cesium atoms back through the microwave cavity. The microwaves partially alter the atomic states of the cesium atoms. http://www.nist.gov/public_affairs/releases/n99-22.cfm Cesium atomic clock Cesium atoms that were altered in the microwave cavity emit light when hit with a laser beam. This fluorescence is measured by a detector (right). The entire process is repeated many times while the microwave energy in the cavity is tuned to different frequencies until the maximum fluorescence of the cesium atoms is determined. This point defines the natural resonance frequency of cesium, which is used to define the second. http://www.nist.gov/public_affairs/releases/n99-22.cfm 18 NIST Cs clock http://www.nist.gov/pml/div688/grp50/primary-frequency-standards.cfm 19 How to build a better clock? 9 192 631 770 periods per second timeandnavigation.si.edu 20 What is a clock? Schematic view of an optical atomic clock: the local oscillator (laser) is resonant with the atomic transition. A correction signal is derived from atomic spectroscopy that is fed back to the laser. An optical frequency synthesizer (optical frequency comb) is used to divide the optical frequency down to countable microwave or radio frequency signals. From: Poli et al. “Optical atomic clocks”, arXiv:1401.2378v2 How good is a clock? There are two principal characteristics that we consider when evaluating state-ofthe-art clocks: stability and uncertainty. Stability is a measure of the precision with which we can measure a quantity (think of how widely scattered a group of arrows red at target might be), and is usually stated as a function of averaging time since for many noise processes the precision increases (i.e., the noise is reduced through averaging) with more measurements. The stability is usually set by the combination of the inherent frequency purity of the physical system and the signal-to-noise ratio with which we can measure the system. In contrast, the (absolute) uncertainty for an atomic clock tells us how well we understand the physical processes that can shift the measured frequency from its unperturbed (“bare"), natural atomic frequency (think of how off-centre our group of arrows might be). Small absolute uncertainty is clearly an essential part of a good primary frequency standard and requires extensive evaluation of all known physical shifts (usually called “systematic effects"). From: Poli et al. “Optical atomic clocks”, arXiv:1401.2378v2 21 Clock unstability Let us first consider the formula for clock instability, σy, in the regime where it is limited by fundamental (as opposed to technical) noise sources, such as atomic statistics based on the number of atoms: spectroscopic linewidth of the clock system the time required for a single measurement cycle the averaging period clock transition frequency the number of atoms or ions used in a single measurement How to build a better clock? 22 Cesium microwave atomic clock Strontium optical atomic clock 9 x 109 periods per second 4.3 x 1014 periods per second http://www.nist.gov/pml/div689/20140122_strontium.cfm Counting optical frequencies Laser frequency (563 nm): Interclock comparisons: • Other optical standards (Al+, Ca, Yb, Sr, etc.) Difference frequency: • Microwave standards Difference frequency: Problem: Fastest electronic counters: Solution: Femtosecond laser frequency comb 33 from Jim Bergquist’ talk 23 from John Hall’s Nobel Lecture fromTheodor W. Hänsch‘s Nobel Lecture 24 Femtosecond Ti:Sapphire Laser Pulsed output Pump laser Pulse duration: Repetition rate: 23 from Jim Bergquist’ talk 25 Strontium optical atomic clock Strontium optical atomic clock http://www.nist.gov/pml/div689/20140122_strontium.cfm 26 Atomic frequency standards Microwave Transitions Optical Transitions Neutral atoms in optical lattices Single ion Th: nuclear clock? Cs: 4×10-16 Sr: 6.4×10-18 M. A. Lombardi, T. Heavner, and S. Jefferts, Measure: J. Meas.Sci. 2, 74 (2007). B. J. Bloom et al., Nature 506, 71 (2014) From: Poli et al. “Optical atomic clocks”, arXiv:1401.2378v2 27 MOTIATION: NEXT GENERATION ATOMIC CLOCKS Next - generation ultra precise atomic clock http://CPEPweb.org Atoms trapped by laser light NIST Yb clock The ability to develop more precise optical frequency standards is essential for new tests of fundamental physics, search for the variation of fundamental constants, and very-long-baseline interferometry for telescope array synchronization. More precise clocks will enable the development of extremely sensitive quantum-based tools for geodesy, hydrology, and climate change studies, inertial navigation, and tracking of deep-space probes. ARE FUNDAMENTAL CONSTANTS CONSTANT??? Being able to compare and reproduce experiments is at the foundation of the scientific approach, which makes sense only if the laws of nature do not depend on time and space. J.-P. Uzan, Rev. Mod. Phys. 75, 403 (2003) 28 Note: we are still measuring them … From NIST Tech Beat: July 19, 2011 29 Which fundamental constants to consider? A pragmatic approach: choose a theoretical framework so that the set of undetermined fixed parameters is fully known. Then, try to determine if these values are constant. It only makes sense to consider the variation of dimensionless ratios: Fine-structure constant α EM = e2 ~ 1/137.036 c Electron or quark mass/QCD strong interaction scale me The electron-proton mass ratio MP me,q Λ QCD … Possible sources for variation of the fundamental constants Unification theories Extra space dimensions Variation of the fundamental constants in an expanding universe Scalar fields ? Life needs very specific fundamental constants! 30 Life needs very specific fundamental constants! α ~1/137 ħ www.economist.com If α is too big → small nuclei can not exist Electric repulsion of the protons > strong nuclear binding force α~1/10 α~1/137 will blow carbon apart Life needs very specific fundamental constants! α ~1/137 ħ www.economist.com α~1/137 Nuclear reaction in stars are particularly sensitive to α. If α were different by 4%: no carbon produced by stars. No life. 31 Life needs very specific fundamental constants! α ~1/137 ħ www.economist.com α~1/132 No carbon produced by stars: No life in the Universe ??? Scientific American Time 21, 70 - 77 (2012) 32 How to test if α changed with time? Atomic transition energies depend on α2 Mg+ ion Scientific American Time 21, 70 - 77 (2012) Astrophysics searches for variation of α: looking for changes in quasar light Scientific American Time 21, 70 - 77 (2012) 33 Julian Berengut, UNSW, 2010 Astrophysical searches for α−variation Alkali-doublet method 3p3/2 ∆EFS ∝ ( Zα ) 3p1/2 2 Observed at red shift z 1 [ ∆EFS ]Z = − 1 α 2 [ ∆EFS ]0 ∆α 3s Na, Mg+, Si3+ Murphy et al. (2001) Observed on Earth ∆α α = −0.5(1.3) ×10−5 34 Astrophysical searches for α−variation Many-multiplet method: compare spectra of different atoms Relativistic correction to the energy Contributions of many-body effects ∆ 1 1 2 ∝ −C ( Zα ) E n* j + 1/ 2 Transition energies depend on α2, Need atomic calculations to find corresponding factor q Observed from quasar absorption spectra α 2 EZ = E0 + q Z − 1 α0 Laboratory frequency Conflicting results Murphy et al., 2003: Keck telescope, 143 systems, 23 lines, 0.2<z<4.2 Quast et al, 2004: VL telescope, 1 system, Fe II, 6 lines ∆α α = −0.4(1.9)(2.7) ×10−6 ∆α α = −0.12(1.8) ×10−6 ∆α α = 5.7(2.7) ×10−6 Molaro et al., 2007 Z=1.84 Srianand et al, 2004: VL telescope, 23 systems, 12 lines, Fe II, Mg I, Si II, Al II, 0.4<z<2.3 Murphy et al., 2007 ∆α α = −0.54(12) ×10 −5 ∆α α = −0.06(0.06) ×10 −5 ∆α α = −0.64(36) ×10−5 V.V. Flambaum, Variation of Fundamental Constants 35 Astrophysical searches for α−variation: the problem of the isotopic abundances On Earth at the present time: 7.6% 92.4% Astrophysical searches for α−variation: the problem of the isotopic abundances Early Universe ?% ?% 36 Astrophysical searches for α−variation: the problem of the isotopic abundances The isotopic abundance ratios in gas clouds in the early universe could vary significantly from those on earth at the present time, and the resulting change in isotope shift (IS) can mimic the variation of α. This effect is similar in magnitude to detected α−variation (Murphy et al., 2003). The separation of the IS from actual α-variation is possible by using “anchor” combinations of atomic frequencies that are insensitive to both effects and “probe‘” combinations of atomic frequencies that are insensitive to IS (Kozlov et al., 2004). Astrophysical searches for α−variation and probes of chemical evolution of the Universe One can form “probe” combinations that are sensitive to only isotope shifts (IS) to measure isotopic abundances in the early universe at the 10-20% level. This is crucially important for testing models of nuclear reactions in stars and supernovae and the chemical evolution of the universe. Use of “probe” and “anchor” combinations requires knowledge of the isotope shifts for lines that can be used in astrophysical studies, including Mg I, Mg II, Si II, Si IV, Ti II, Cr II, Fe II, Ni II, Zn II, and Ge II. Very few IS measurements exist in these systems. Present IS accuracy that varies from 2% for Mg I to 70% for Ni II is insufficient. 37 Can we look for α−variation in a lab? Different optical atomic clocks use transitions that have different contributions of the relativistic corrections to frequencies. Therefore, comparison of these clocks can be used to search for α−variation. The most precise laboratory test of α−variation has been carried out at NIST [1] by measuring the frequency ratio of Al+ and Hg+ optical atomic clocks with a fractional uncertainty of 5.2×10-17. Repeated measurements during the year yielded a constraint on the temporal variation of α α = −1.6(2.3) × 10−17. [1] T. Rosenband et al.,Science 319, 1808 (2008). 38 Laboratory searches for α−variation Different atomic clocks use transitions that have different contributions of the relativistic corrections to frequencies. ν ( x) = ν 0 + qx 2 x = (α α 0 ) − 1 Therefore, comparison of different clocks can be used to search for α−variation. NIST [Rosenband et al., Science 319, 1808 (2008)] Al+ / Hg+ atomic clocks α α = −1.6(2.3) ×10−17 y −1 199Hg+ Energy Levels 5d106p 5d96s2 5d106s • Atomic line • State detection by electron shelving. 3 from Jim Bergquist’ talk 39 Trapped ions in an rf trap • No static E or B fields; Trap acts on total charge of ion, not internal structure • Trap ion at trap center where trapping fields approach zero ~ rf • Can operate in tight-confinement (Lamb-Dicke) regime ⇒ First-order doppler free. 2nd-order doppler shift (time dilation) due to micromotion will limit accuracy from Jim Bergquist’ talk 11 Liquid Nitrogen Magnetic Shield Cryostat Wall 77 K Shield Liquid Helium Helical Resonator 4 K Copper Shield around trap 13 • Long storage times • Environmental isolation - Low collision rate - Low blackbody from Jim Bergquist’ talk 40 Some facts about Al+ 1P 1 3P • 8 mHz linewidth clock transition 167 nm 267 nm 1121 THz • Small quadratic ZS (6x10-16 /Gauss2) • Negligible electric-quadrupole shift (J=0) 1S 0 0 • Smallest known blackbody shift (8x10-18 at 300K) I = 5/2 • Linear ZS 4 kHz/Gauss (easily compensated) • Light mass (2nd order Doppler shifts) • No accessible strong transition for cooling & state detection from Jim Bergquist’ talk Clock state transfer to Be+ (simplified) 1. Cool to motional quantum ground state with Be+ 2. Depending on clock state, add vibrational energy via Al+ 3. Detect vibrational energy via Be+ from Jim Bergquist’ talk 41 Using two ions Clock ion (Al+) for very accurate spectroscopy Logic ion (Be+) for cooling and readout Coulomb-force couples the motion of the ions ⇒ Cooling Be+ leads to cooling of Al+ Ion motion is quantized (n=0, 1, …) Transfer information Al+ Motion Be+ from Jim Bergquist’ talk from Jim Bergquist’ talk Al+/Hg+ Comparison fs-comb locked to Hg+ measure beat with Al+ 1126 nm laser 1070 nm laser fiber ×2 ×2 fiber ×2 199Hg Hg++ ×2 fb,Hg n frep+ fceo 9Be+ fb,Al 27Al+ m frep+ fceo 42 from Jim Bergquist’ talk Al+/Hg+ Comparison -17 νAl/νHg × 10 15 - 1 052 871 833 148 990 α-dot / α = (1.433 +/- 1.702) x 10 2 / yr χ =2.9674 0.5 10-16 0.4 2006 2007 2007 Dec Jan FebMar Apr May Jun Jul Aug Sep Oct Nov Dec NEED MORE PRECISE FREQUENCY STANDARDS: NEW CLOCK PROPOSALS 43 Electronic bridge: How to run Th3+ nuclear clock? Th nuclear clock: Nuclear isomer transition in 229 Thorium has been suggested as an etalon transition in a new type of optical frequency standard. Need calculations to find usable electronic transitions. Correlation and relativistic effects in actinide ions, M. S. Safronova and U. I. Safronova, Phys. Rev. A 84, 052515 (2011). HIGHLYHIGHLY-CHARGED IONS ??? 100 Cl6+ 102 nm 200 300 400 500 Al+ 267 nm 600 Wavelength nm Mg 458 nm Si2+ 190 nm 3s2 1S0 – 3s3p 3P0 transition in Mg-like ions 44 HIGHLYHIGHLY-CHARGED IONS ! Optical transitions are possible due to level crossings ! Sn-like ions (current work) [Kr] 4d105s2 core Sn 5p6s 3P0 5p2 1S0 1D 289 nm 2 2 3 5p P0,1,2 Sn –like Ba6+ 5p2 1S0 1D 2 3P 2 3P 1 5p2 3P0 Sn-like Pr9+ 5p4f J=3 163 nm 495(13) nm 5p2 3P0 45