DOCSLIB.ORG

Transition Dipole Moment Measurements of Ultracold Photoassociated 85Rb133cs Molecules by Depletion Spectroscopy ∗

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Transition Dipole Moment Measurements of Ultracold Photoassociated 85Rb133cs Molecules by Depletion Spectroscopy ∗ CHIN. PHYS. LETT. Vol. 35, No. 10 (2018) 103301 Transition Dipole Moment Measurements of Ultracold Photoassociated 85Rb133Cs Molecules by Depletion Spectroscopy ∗ Juan-Juan Cao(曹娟娟)1;2, Ting Gong(宫廷)1;2, Zhong-Hao Li(李中豪)1;2, Zhong-Hua Ji(姬中华)1;2**, Yan-Ting Zhao(赵延霆)1;2, Lian-Tuan Xiao(肖连团)1;2, Suo-Tang Jia(贾锁堂)1;2 1State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006 2Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006 (Received 6 July 2018) The transition dipole moments (TDMs) of ultracold 85Rb133Cs molecules between the lowest vibrational ground 1 + 3 0 0 1 0 level, X Σ (v = 0, J = 1), and the two excited rovibrational levels, 2 Π0+ (v = 10, J = 2) and 2 Π1 (v = 22, J 0 = 2), are measured using depletion spectroscopy. The ground-state 85Rb133Cs molecules are formed from 3 cold mixed component atoms via the 2 Π0− (v = 11, J = 0) short-range level, then detected by time-of-flight mass spectrum. A home-made external-cavity diode laser is used as the depletion laser to couple the ground level and the two excited levels. Based on the depletion spectroscopy, the corresponding TDMs are then derived −3 −2 to be 3.5(2)×10 ea0 and 1.6(1)×10 ea0, respectively, where ea0 represents the atomic unit of electric dipole 1 0 0 moment. The enhance of TDM with nearly a factor of 5 for the 2 Π1 (v = 22, J = 2) excited level means that it has stronger coupling with the ground level. It is meaningful to find more levels with much more strong coupling strength by the represented depletion spectroscopy to realize direct stimulated Raman adiabatic passage transfer from scattering atomic states to deeply molecular states. PACS: 33.80.−b, 32.70.Cs, 32.80.−t DOI: 10.1088/0256-307X/35/10/103301 Ultracold molecules have attracted widespread at- for other heteronuclear molecules. This is an obsta- tention in recent years. Compared with homonu- cle to transferring mixed cooled atoms directly to the clear molecules, heteronuclear (or polar) molecules deeply bound molecular state. Thus it is meaningful have unique properties: tunable, long-range and to search for more suitable excited PA states which anisotropic dipole-dipole interaction. These proper- have both singlet and triplet characters for efficiently ties mean ultracold polar molecules have many impor- producing and transfering molecules from atoms. Re- 1 tant applications, such as ultracold chemistry, quan- cently, Shimasaki et al. studied such mixed 2 Π1- 3 3 + [18] tum computer, quantum simulation and precision 2 Π1-3 Σ1 states. It is found that the product rate measurement.[1;2] is comparative with the previous value of two-photon Up to date, the methods to prepare ultra- cascade decay, and the direct spontaneous decay may cold molecules include photoassociation (PA) by play an important role due to the mixed characters. [3] [4] 1 continuous and shaped laser, magentoassocia- Especially for the 2 Π1 state, it has mainly a single tion (MA)[5] or spin-orbit coupling[6] from precooled character and may have stronger coupling with the atoms, and direct laser cooling[7] from preexisting ground state. Thus we need to measure the corre- molecules. Especially in recent years the short-range sponding transition dipole moments (TDMs), which PA, due to the merit of direct formation, continuous represent the strength of transition between the ini- accumulation and potential direct stimulated Raman tial and final states, and compare the values for the 3 adiabatic passage (STIRAP) transfer from scattering 2 Π0+ state. atomic states to deeply molecular states,[8;9] is veri- Many effective methods have been used to measure fied to be an interesting alternative pathway to pro- the TDM of atoms and molecules before, such as two- duce cold polar molecules in the lowest vibrational photon dark resonance spectroscopy,[19] electromag- ground state (v = 0).[10−17] Among these molecules, netically induced transparency,[20] and Autler–Townes 85Rb133Cs[13−16] (hereafter superscript will be omit- splitting.[21] All of these systems involve three or four ted) is particularly interesting due to several distinc- energy levels. Also, a number of samples are usually tive merits, including chemical stability, considerable needed to obtain a good signal-to-noise ratio (SNR). permanent electric dipole moment, and low cost. In However, the number of experimentally formed cold addition, the molecule product rate is also consid- molecules is ordinarily on the order of thousands or erable. However, the formed mechanism for RbCs even fewer, which will limit the SNR based on these molecules decays through a two-photon cascade decay, methods. Usually a rapid, sensitive photoionization which is different from a one-step spontaneous decay (PI) spectroscopy is used to detect the formed cold ∗Supported by the National Key Research and Development Program of China under Grant No 2017YFA0304203, the National Natural Science Foundation of China under Grant Nos 61675120 and 11434007, the National Natural Science Foundation of China for Excellent Research Team under Grant No 61121064, the Shanxi Scholarship Council of China, the 1331KSC, the PCSIRT under Grant No IRT13076, and the Applied Basic Research Project of Shanxi Province under Grant No 201601D202008. **Corresponding author. Email: [email protected] © 2018 Chinese Physical Society and IOP Publishing Ltd 103301-1 CHIN. PHYS. LETT. Vol. 35, No. 10 (2018) 103301 molecules with vibrational resolution. To realize the in the X1Σ + (v = 0, J = 1) ground level. (i) First rotational resolution of ground state molecules, a de- of all, the loading procedure (the duration time of pletion spectroscopy is firstly introduced by Wang et 90 ms) of dark-SPOTs and PA procedure occur si- [22] 3 al. and has been widely used in recent years. As the multaneously to produce the molecules in the 2 Π0− depletion laser couples molecules between the ground (v = 11, J = 0) level. The PA laser (typical state and excited states, it is also suitable to measure linewidth of 100 kHz, output power of 1.5 W, Gaus- the corresponding TDM between them. sian radius of 150 µm) is locked by a subtle transfer In this work, we measure the transition dipole mo- cavity technique.[26] (ii) At the same time with (i), ments for 85Rb133Cs molecules from the lowest vibra- the molecules are distributing in different vibrational tional state, X1Σ + (v = 0) to different excited states, ground states after the two-photon-cascade sponta- 3 0 1 0 1 + 2 Π0+ (v = 10) and 2 Π1 (v = 22). The former of neous emission process, including the X Σ (v = 0, the excited states can produce ground-state RbCs mo- J = 1) level. (iii) Then all the dark-SPOT lasers and elecules via two-photon cascade decay while the lat- PA laser are turned off. Meanwhile, the depletion laser 3 3 + ter has strong spin-orbit mixing with 2 Π1 and 3 Σ1 is turned on for several ms to couple the transition 1 + 3 0 states, and thus may have more strong one-step spon- from the X Σ (v = 0) state to the 2 Π0+ (v = 10), 1 0 taneous decay due to strong coupling with the ground or 2 Π1 (v = 22) state. The depletion laser frequency state. The corresponding TDM is derived by fitting (linewidth of 2 MHz, actual power of up to 10 mW) the dependence of depletion ratio on both power and can be controlled based on the same transfer cavity irradiated time of depletion laser to the classical ab- technique. To locate the accurate depletion laser fre- sorption formula for a two-level system. The TDM for quency, the rotational levels of two upper states are 1 0 2 Π1 (v = 22) with a factor of 5 larger than the value measured with the PA spectrum in advance, as shown 3 0 for 2 Π0+ (v = 10) is observed, verifying the much in Figs.1(b) and1(c). The spectral widths are fitted to stronger mixing with the ground state. be 17(2) MHz and 200(10) MHz by single-peak Lorentz Most details of the apparatus have been described and multi-peaks Lorentz formulas, respectively. The [23] [15;16] 1 0 before, such as in our recent and previous large width for the 2 Π1 (v = 22) state arises works. The starting point for this work is a mix- from the hyperfine structure.[18] (iv) The PI laser ture of laser cooled 85Rb and Cs atoms in space- (pulse energy of around 1 mJ, pulse duration of 7 ns, adjustable dark spontaneous force optical traps (dark- linewidth of 6 GHz, diameter of about 3 mm) with res- SPOTs).[24] Under a vacuum background pressure of onant transition between X1Σ + (v = 0) and 21Π around 3×10−7 Pa and a magnetic gradient of around (v = 12)[15] is used to photoionize the formed ground- 15 G/cm, we trap mixed atomic clouds with about state molecules through one color resonance-enhanced 7 85 [27] 1 × 10 Rb atoms in the 5S1=2 (F = 2) state with a two-photon ionization (RETPI). The photoionized density of 8 × 1010 cm−3, and about 2 × 107 133Cs molecular ions are then accelerated by a pulsed ac- atoms in the 6S1=2 (F = 3) state with a density celerating electric field and detected by a pair of mi- of 1 × 1011 cm−3. The translational temperature of cro channel plates (MCPs). The repetition rate is the mixed atoms is measured by time-of-flight (TOF) 10 Hz in our experiment. To obtain depletion spec- imaging to be around 100 µK.
Load more

Recommended publications
  • Magnetism, Angular Momentum, and Spin
    Chapter 19 Magnetism, Angular Momentum, and Spin P. J. Grandinetti Chem. 4300 P. J. Grandinetti Chapter 19: Magnetism, Angular Momentum, and Spin In 1820 Hans Christian Ørsted discovered that electric current produces a magnetic field that deflects compass needle from magnetic north, establishing first direct connection between fields of electricity and magnetism. P. J. Grandinetti Chapter 19: Magnetism, Angular Momentum, and Spin Biot-Savart Law Jean-Baptiste Biot and Félix Savart worked out that magnetic field, B⃗, produced at distance r away from section of wire of length dl carrying steady current I is 휇 I d⃗l × ⃗r dB⃗ = 0 Biot-Savart law 4휋 r3 Direction of magnetic field vector is given by “right-hand” rule: if you point thumb of your right hand along direction of current then your fingers will curl in direction of magnetic field. current P. J. Grandinetti Chapter 19: Magnetism, Angular Momentum, and Spin Microscopic Origins of Magnetism Shortly after Biot and Savart, Ampére suggested that magnetism in matter arises from a multitude of ring currents circulating at atomic and molecular scale. André-Marie Ampére 1775 - 1836 P. J. Grandinetti Chapter 19: Magnetism, Angular Momentum, and Spin Magnetic dipole moment from current loop Current flowing in flat loop of wire with area A will generate magnetic field magnetic which, at distance much larger than radius, r, appears identical to field dipole produced by point magnetic dipole with strength of radius 휇 = | ⃗휇| = I ⋅ A current Example What is magnetic dipole moment induced by e* in circular orbit of radius r with linear velocity v? * 휋 Solution: For e with linear velocity of v the time for one orbit is torbit = 2 r_v.
    [Show full text]
  • Oscillator Strength ( F ): Quantum Mechanical Model
    Oscillator strength ( f ): quantum mechanical model • For an electronic transition to occur an oscillating dipole must be induced by interaction of the molecules electric field with electromagnetic radiation. 0 • In fact both ε and k can be related to the transition dipole moment (µµµge ) • If two equal and opposite electrical charges (e) are separated by a vectorial distance (r), a dipole moment (µµµ ) of magnitude equal to er is created. µµµ = e r (e = electron charge, r = extent of charge displacement) • The magnitude of charge separation, as the electron density is redistributed in an electronically excited state, is determined by the polarizability (αααα) of the electron cloud which is defined by the transition dipole moment (µµµge ) α = µµµge / E (E = electrical force) µµµge = e r • The magnitude of the oscillator strength ( f ) for an electronic transition is proportional to the square of the transition dipole moment produced by the action of electromagnetic radiation on an electric dipole. 2 2 f ∝ µµµge = ( e r) fobs = fmax ( fe fv fs ) 2 f ∝ µµµge fobs = observed oscillator strength f ∝ ΛΏΦ ∆̅ !2#( fmax = ideal oscillator strength ( ∼1) f = orbital configuration factor ͯͥ e f ∝ ͤ͟ ̅ ͦ Γ fv = vibrational configuration factor fs = spin configuration factor • There are two major contributions to the electronic factor fe : Poor overlap: weak mixing of electronic wavefunctions, e.g. <nπ*>, due to poor spatial overlap of orbitals involved in the electronic transition, e.g. HOMO→LUMO. Symmetry forbidden: even if significant spatial overlap of orbitals exists, the resonant photon needs to induce a large transition dipole moment.
    [Show full text]
  • Spontaneous Rotational Symmetry Breaking in a Kramers Two- Level System
    Spontaneous Rotational Symmetry Breaking in a Kramers Two- Level System Mário G. Silveirinha* (1) University of Lisbon–Instituto Superior Técnico and Instituto de Telecomunicações, Avenida Rovisco Pais, 1, 1049-001 Lisboa, Portugal, [email protected] Abstract Here, I develop a model for a two-level system that respects the time-reversal symmetry of the atom Hamiltonian and the Kramers theorem. The two-level system is formed by two Kramers pairs of excited and ground states. It is shown that due to the spin-orbit interaction it is in general impossible to find a basis of atomic states for which the crossed transition dipole moment vanishes. The parametric electric polarizability of the Kramers two-level system for a definite ground-state is generically nonreciprocal. I apply the developed formalism to study Casimir-Polder forces and torques when the two-level system is placed nearby either a reciprocal or a nonreciprocal substrate. In particular, I investigate the stable equilibrium orientation of the two-level system when both the atom and the reciprocal substrate have symmetry of revolution about some axis. Surprisingly, it is found that when chiral-type dipole transitions are dominant the stable ground state is not the one in which the symmetry axes of the atom and substrate are aligned. The reason is that the rotational symmetry may be spontaneously broken by the quantum vacuum fluctuations, so that the ground state has less symmetry than the system itself. * To whom correspondence should be addressed: E-mail: [email protected] -1- I. Introduction At the microscopic level, physical systems are generically ruled by time-reversal invariant Hamiltonians [1].
    [Show full text]
  • PHYSICAL SPECTROSCOPY) MODULE No. : 5 (TRANSITION PROBABILITIES and TRANSITION DIPOLE MOMENT. OVERVIEW of SELECTION RULES
    ____________________________________________________________________________________________________ Subject Chemistry Paper No and Title 8 and Physical Spectroscopy Module No and Title 5 and Transition probabilities and transition dipole moment, Overview of selection rules Module Tag CHE_P8_M5 CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 5 (TRANSITION PROBABILITIES AND TRANSITION DIPOLE MOMENT. OVERVIEW OF SELECTION RULES) ____________________________________________________________________________________________________ TABLE OF CONTENTS 1. Learning Outcomes 2. Introduction 3. Transition Moment Integral 4. Overview of Selection Rules 5. Summary CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 5 (TRANSITION PROBABILITIES AND TRANSITION DIPOLE MOMENT. OVERVIEW OF SELECTION RULES) ____________________________________________________________________________________________________ 1. Learning Outcomes After studying this module, • you shall be able to understand the basis of selection rules in spectroscopy • Get an idea about how they are deduced. 2. Introduction The intensity of a transition is proportional to the difference in the populations of the initial and final levels, the transition probabilities given by Einstein’s coefficients of induced absorption and emission and to the energy density of the incident radiation. We now examine the Einstein’s coefficients in some detail. 3. Transition Dipole Moment Detailed algebra involving the time-dependent perturbation theory allows us to derive a theoretical expression for the Einstein coefficient of induced absorption ! 2 3 M ij 8π ! 2 B M ij = 2 = 2 ij 6ε 0" 3h (4πε 0 ) where the radiation density is expressed in units of Hz. ! The quantity M ij is known as the transition moment integral, having the same unit as dipole moment, i.e. C m. Apparently, if this quantity is zero for a particular transition, the transition probability will be zero, or, in other words, the transition is forbidden.
    [Show full text]
  • Chapter 14 Radiating Dipoles in Quantum Mechanics
    Chapter 14 Radiating Dipoles in Quantum Mechanics P. J. Grandinetti Chem. 4300 P. J. Grandinetti Chapter 14: Radiating Dipoles in Quantum Mechanics P. J. Grandinetti Chapter 14: Radiating Dipoles in Quantum Mechanics Electric dipole moment vector operator Electric dipole moment vector operator for collection of charges is ∑N ⃗̂휇 ⃗̂ = qkr k=1 Single charged quantum particle bound in some potential well, e.g., a negatively charged electron bound to a positively charged nucleus, would be [ ] ⃗̂휇 ⃗̂ ̂⃗ ̂⃗ ̂⃗ = *qer = *qe xex + yey + zez Expectation value for electric dipole moment vector in Ψ(⃗r; t/ state is ( ) ê ⃗휇 ë < ⃗; ⃗̂휇 ⃗; 휏 < ⃗; ⃗̂ ⃗; 휏 .t/ = Ê Ψ .r t/ Ψ(r t/d = Ê Ψ .r t/ *qer Ψ(r t/d V V Here, d휏 = dx dy dz P. J. Grandinetti Chapter 14: Radiating Dipoles in Quantum Mechanics Time dependence of electric dipole moment Energy Eigenstate Starting with ( ) ê ⃗휇 ë < ⃗; ⃗̂ ⃗; 휏 .t/ = Ê Ψ .r t/ *qer Ψ(r t/d V For a system in eigenstate of Hamiltonian, where wave function has the form, ` ⃗; ⃗ *iEnt_ Ψn.r t/ = n.r/e Electric dipole moment expectation value is ( ) ` ` ê ⃗휇 ë < ⃗ iEnt_ ⃗̂ ⃗ *iEnt_ 휏 .t/ = Ê n .r/e *qer n.r/e d V Time dependent exponential terms cancel out leaving us with ( ) ê ⃗휇 ë < ⃗ ⃗̂ ⃗ 휏 .t/ = Ê n .r/ *qer n.r/d No time dependence!! V No bound charged quantum particle in energy eigenstate can radiate away energy as light or at least it appears that way – Good news for Rutherford’s atomic model.
    [Show full text]
  • Decoupling Light and Matter: Permanent Dipole Moment Induced Collapse of Rabi Oscillations
    Decoupling light and matter: permanent dipole moment induced collapse of Rabi oscillations Denis G. Baranov,1, 2, ∗ Mihail I. Petrov,3 and Alexander E. Krasnok3, 4 1Department of Physics, Chalmers University of Technology, 412 96 Gothenburg, Sweden 2Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny 141700, Russia 3ITMO University, St. Petersburg 197101, Russia 4Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, Texas 78712, USA (Dated: June 29, 2018) Rabi oscillations is a key phenomenon among the variety of quantum optical effects that manifests itself in the periodic oscillations of a two-level system between the ground and excited states when interacting with electromagnetic field. Commonly, the rate of these oscillations scales proportionally with the magnitude of the electric field probed by the two-level system. Here, we investigate the interaction of light with a two-level quantum emitter possessing permanent dipole moments. The semi-classical approach to this problem predicts slowing down and even full suppression of Rabi oscillations due to asymmetry in diagonal components of the dipole moment operator of the two- level system. We consider behavior of the system in the fully quantized picture and establish the analytical condition of Rabi oscillations collapse. These results for the first time emphasize the behavior of two-level systems with permanent dipole moments in the few photon regime, and suggest observation of novel quantum optical effects. I. INTRODUCTION ment modifies multi-photon absorption rates. Emission spectrum features of quantum systems possessing perma- Theory of a two-level system (TLS) interacting with nent dipole moments were studied in Refs.
    [Show full text]
  • Lecture 13 Page 1 Note That Polarizability of Classical Conductive Sphere of Radius a Is
    Lectures 13 - 14 Hydrogen atom in electric field. Quadratic Stark effect. Atomic polarizability. Emission and Absorption of Electromagnetic Radiation by Atoms Transition probabilities and selection rules. Lifetimes of atomic states. Hydrogen atom in electric field. Quadratic Stark effect. We consider a hydrogen atom in the ground state in the uniform electric field The Hamiltonian of the system is [using CGS units] orienting the quantization axis (z) along the electric field. Since d is odd operator under the parity transformation r → -r even function product Therefore, need second-order correction to the energy We will use the approximation Note that we included 100 term to make use of the completeness relation since it is zero anyway. Lecture 13 Page 1 Note that polarizability of classical conductive sphere of radius a is Lecture 13 Page 2 Emission and Absorption of Electromagnetic Radiation by Atoms (follows W. Demtr öder, chapter 7) During the past few lectures, we have discussed stationary atomic states that are described by a stationary wave function and by the corresponding quantum numbers. We also discussed the atoms can undergo transitions between different states with energies E i and E , when a photon with energy k (1) is emitted or absorbed. We know from the experiments, however, that the absorption or emission spectrum of an atom does not contain all possible frequencies ω according to the formula above . Therefore, t here must be “selection rules” that select the possible radiative transitions from all combinations of E i and E k. These selection rules strongly affect the lifetimes of the atomic excited states.
    [Show full text]
  • Chapter 15 the Tools of Time-Dependent Perturbation Theory Can Be Applied to Transitions Among Electronic, Vibrational, and Rotational States of Molecules
    Chapter 15 The tools of time-dependent perturbation theory can be applied to transitions among electronic, vibrational, and rotational states of molecules. I. Rotational Transitions Within the approximation that the electronic, vibrational, and rotational states of a molecule can be treated as independent, the total molecular wavefunction of the "initial" state is a product F i = y ei c vi f ri of an electronic function y ei, a vibrational function c vi, and a rotational function f ri. A similar product expression holds for the "final" wavefunction F f. In microwave spectroscopy, the energy of the radiation lies in the range of fractions of a cm-1 through several cm-1; such energies are adequate to excite rotational motions of molecules but are not high enough to excite any but the weakest vibrations (e.g., those of weakly bound Van der Waals complexes). In rotational transitions, the electronic and vibrational states are thus left unchanged by the excitation process; hence y ei = y ef and c vi = c vf. Applying the first-order electric dipole transition rate expressions Ri,f = 2 p g(wf,i) |a f,i|2 obtained in Chapter 14 to this case requires that the E1 approximation Ri,f = (2p/h2) g(wf,i) | E0 · <F f | m | F i> |2 be examined in further detail. Specifically, the electric dipole matrix elements <F f | m | F i> with m = S j e rj + S a Za e Ra must be analyzed for F i and F f being of the product form shown above. The integrations over the electronic coordinates contained in <F f | m | F i>, as well as the integrations over vibrational degrees of freedom yield "expectation values" of the electric dipole moment operator because the electronic and vibrational components of F i and F f are identical: <y ei | m | y ei> = m (R) is the dipole moment of the initial electronic state (which is a function of the internal geometrical degrees of freedom of the molecule, denoted R); and <c vi | m(R) | c vi> = mave is the vibrationally averaged dipole moment for the particular vibrational state labeled c vi.
    [Show full text]
  • Electric Dipole Moment and Therefore Can Be Excited by Either a Photon Or an Electron
    Chem 253, UC, Berkeley Fermi Surface E 2k 2 F E(k) x 2m K KF a2 r 2 2 r 0.4a Chem 253, UC, Berkeley With periodic boundary conditions: ik L eikx Lx e y y eikz Lz 1 2nx kx Lx 2n k y 2 2 y 2D k space: Ly Area per k point: L L 2nz x y kz Lz 2 2 2 8 3 3D k space: Area per k point: Lx Ly Lz V V A region of k space of volume will contain: allowed 8 3 8 3 k values. ( ) V 1 Chem 253, UC, Berkeley For divalent elements: free –electron model a2 r 2 r 0.56a Chem 253, UC, Berkeley 2 Chem 253, UC, Berkeley For nearly free electron: 1. Interaction of electron with periodic potential opens gap at zone boundary 2. Almost always Fermi surface will intersect zone Boundaries perpendicularly. 3. The total volume enclosed by the Fermi surface depends only on total electron concentration, not on interaction Chem 253, UC, Berkeley Alkali Metal Na, Cs: spherical Fermi surface a2 r 2 2 r 0.4a Alk. Earth metal: Be, Mg:: nearly spherical Fermi surface a2 r 2 r 0.56a 2D case 3 Chem 253, UC, Berkeley Chem 253, UC, Berkeley 4 Chem 253, UC, Berkeley Chem 253, UC, Berkeley 5 Chem 253, UC, Berkeley Chem 253, UC, Berkeley 6 Chem 253, UC, Berkeley Chem 253, UC, Berkeley 7 Chem 253, UC, Berkeley Brillouin Zone of Diamond and Zincblende Structure (FCC Lattice) Sign Convention Zone Edge or surface : Latin alphabets Interior of Zone: Greek alphabets Center of Zone or origin: Chem 253, UC, Berkeley Band Structure of 3D Free Electron in FCC in reduced zone scheme Notation: <=>[100] direction X<=>BZ edge along [100] direction <=>[111] direction E(k)=( 2/2m)
    [Show full text]
  • Ultracold Rare-Earth Magnetic Atoms with an Electric Dipole Moment
    Ultracold rare-earth magnetic atoms with an electric dipole moment Maxence Lepers1,2, Hui Li1, Jean-Fran¸cois Wyart1,3, Goulven Qu´em´ener1 and Olivier Dulieu1 1Laboratoire Aim´eCotton, CNRS, Universit´eParis-Sud, ENS Paris-Saclay, Universit´eParis-Saclay, 91405 Orsay, France 2Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Universit´ede Bourgogne Franche-Comt´e, 21078 Dijon, France∗ and 3LERMA, Observatoire de Paris-Meudon, PSL Research University, Sorbonne Universit´es, UPMC Univ. Paris 6, CNRS UMR8112, 92195 Meudon, France (Dated: March 13, 2018) We propose a new method to produce an electric and magnetic dipolar gas of ultracold dysprosium − atoms. The pair of nearly degenerate energy levels of opposite parity, at 17513.33 cm 1 with − electronic angular momentum J = 10, and at 17514.50 cm 1 with J = 9, can be mixed with an external electric field, thus inducing an electric dipole moment in the laboratory frame. For field amplitudes relevant to current-day experiments, we predict a magnetic dipole moment up to 13 Bohr magnetons, and an electric dipole moment up to 0.22 Debye, which is similar to the values obtained for alkali-metal diatomics. When a magnetic field is present, we show that the electric dipole moment is strongly dependent on the angle between the fields. The lifetime of the field- mixed levels is found in the millisecond range, thus allowing for suitable experimental detection and manipulation. Introduction. In a classical neutral charge distribu- with an electric and a magnetic dipole moment, which up tion, a dipole moment appears with a separation be- to now consist of paramagnetic polar diatomics [23–32].
    [Show full text]
  • CHAPTER 12 Molecular Spectroscopy 1: Rotational and Vibrational Spectra
    CHAPTER 12 Molecular Spectroscopy 1: Rotational and Vibrational Spectra I. General Features of Spectroscopy. A. Overview. 1. Bohr frequency rule: hc Ephoton = hν = = hcν˜ = Eupper −Elower λ 1 Also remember ν˜ = (usually in cm-1) λ € 2. Types of spectroscopy (three broad types): -emission € -absorption -scattering Rayleigh Stokes Anti-Stokes CHAPTER 12 1 3. The electromagnetic spectrum: Region λ Processes gamma <10 pm nuclear state changes x-ray 10 pm – 10 nm inner shell e- transition UV 10 nm – 400 nm electronic trans in valence shell VIS 400 – 750 nm electronic trans in valence shell IR 750 nm – 1 mm Vibrational state changes microwave 1 mm – 10 cm Rotational state changes radio 10 cm – 10 km NMR - spin state changes 4. Classical picture of light absorption – since light is oscillating electric and magnetic field, interaction with matter depends on interaction with fluctuating dipole moments, either permanent or temporary. Discuss vibrational, rotational, electronic 5. Quantum picture: Einstein identified three contributions to transitions between states: a. stimulated absorption b. stimulated emission c. spontaneous emission Stimulated absorption transition probability w is proportional to the energy density ρ of radiation through a proportionality constant B w=B ρ The total rate of absorption W depends on how many molecules N in the light path, so: W = w N = N B ρ CHAPTER 12 2 Now what is B? Consider plane-polarized light (along z-axis), can cause transition if the Q.M. transition dipole moment is non-zero. µ = ψ *µˆ ψdτ ij ∫ j z i Where µˆ z = z-component of electric dipole operator of atom or molecule Example: H-atom € € - e r + µˆ z = −er Coefficient of absorption B (intrinsic ability to absorb light) 2 µij B = 6ε 2€ Einstein B-coefficient of stimulated absorption o if 0, transition i j is allowed µ ij ≠ → µ = 0 forbidden € ij € 6.
    [Show full text]
  • Coherent Optical Spectroscopy of a Single Semi- Conductor Quantum Dot
    COHERENT OPTICAL SPECTROSCOPY OF A SINGLE SEMI- CONDUCTOR QUANTUM DOT by Xiaodong Xu A dissertation submitted in partial ful¯llment of the requirements for the degree of Doctor of Philosophy (Physics) in The University of Michigan 2008 Doctoral Commitee: Professor Duncan G. Steel, Chair Professor Roberto D. Merlin Professor Theodore B. Norris Professor Georg A. Raithel Associate Professor Luming Duan Xiaodong Xu °c 2008 All Rights Reserved ACKNOWLEDGEMENTS 6 years ago when I joined the group, Elaine gave me a lab tour. I saw Jun and Yanwen sitting in the dark and taking data. At that time there was a big chiller in the time domain lab and making huge noise. Frankly, I was a bit scared since I had never been in a real lab before graduate school. I was wondering whether I could do well in such a lab as an experimental physicist. Now it is 6 years later and I am so happy to say that I made it. During the entire graduate school, there are so many people I would like to thank. The ¯rst and the most important person I would like to thank is my advisor Professor Duncan Steel. I am so lucky to have Duncan as my advisor. He is such a smart scientist with great personality. His working ethics and conscientious attitudes inspired me a lot in research. He always tries to create the best education and research support for me. One of the greatest things is that he tried to develop my weakness, exploit my strength, and carefully shape me to be a good physicist.
    [Show full text]