Stimulated Rapid Adiabatic Passage of Metastable Helium: Principle and Operation

Transcription

1 Stimulated Rapid Adiabatic Passage of Metastable Helium: Principle and Operation YUAN SUN DEPARTMENT OF PHYSICS & ASTRONOMY STATE UNIVERSITY OF NEW YORK AT STONY BROOK

2 What is Stimulated Rapid Adiabatic Passage? Usually it is called STIRAP First Introduced by K. Bergmann & co-workers at 1988: Population switching between vibrational levels in molecular beams, Chem. Phys. Lett. 149, 463 Coherent control of atoms: coherent efficient population transfer.

3 What is Stimulated Rapid Adiabatic Passage? In practice, it is pulses of counter intuitive order

4 Two Methods of Realization Atoms still; Laser pulsed Atoms moving; CW Laser

5 Different Energy level configurations are OK Λ Configuration Ladder Configuration

6 Table of Contents Metastable Helium Rotating wave frame, 2 level atom and Adiabatic States 3 level system and STIRAP Stark effect for Rydberg states Parameters that influence STIRAP performance Laser system: Frequency doubling Laser system: SAS & PDH Efficiency measurement: Curved wave front

7 Why Helium? Helium 4 is used in our experiment; High purification; No hyperfine structure; When one electron is excited, it behaves like an atom with a single electron

8 Metastable Helium: Energy Level Metastable Groud State He* By discharging

9 The source produces He* atoms with v l =1070±220 m / s and a flux of ~0.5*10 14 atoms / sr s Metastable Helium: Source Design

10 The Source when Discharging

11 Source Parameters: Varying Flow Pressure

12 Source Parameters: Varying Discharging Voltage

13 Physics of Coherent Manipulation of Atoms TIME DEPENDENT SCHRÖDINGER EQUATION

14 Rotating Wave Frame You manually add a phase term to each coefficient. It is a little different from Interaction Picture since you may actually choose what this phase is. The purpose is to acquire a good equation of motion for the coefficients. Suppose we already have a complete set of eigenstates. Start from : i α >= H α >, H = H ( t); t α >= n >< n α >= < n α > e e n > iζn() t iζn() t ( ) ( ) ; n n iζ n () t Let Cn() t = e < n α >, d Get i C t = ζ t C t + e e H C t dt where H =< n H m > iζn() t iζm() t : n() n() n() nm m(), nm

15 The Rotating Wave Frame: General Form given α >= ( n >< n ) α >= K ( t) n >, α >= α, t > n it satisfies : i K () t = H K ();[..] t i e i K = HK; n nm m now perform a transform : B () t = U () t K ();[..] t i e B = UK; what is the equation of motion of B? [ ie..] i B 1 1 = ( i UU + UHU ) B What is this U as rlated to basis tranf? Say n R m Then U R Total probability is conserved! n n nm m T 1 : >= nm >, = ; It is normal to require R is unitary, hence generally U is unitary too. n

16 Two Level Atoms IS IT REALLY VERY SIMPLE? Excited level Ground level

17 Set up the Hamiltonian i α >= H α > t where H = H + H, H = µ E( t); 0 I Use the usual 1&2 energy eigenstate as basis : E1 0 0 µ 12 Et () H0 =, HI = ; 0 E2 µ 21 Et () 0 with µ =< i µ j> ; ij I

18 Entering the Rotating Frame Describe the electric field: iωt 1 iωt * iωt Et () = Re( eete () ) = ε()[ t e e + e e ] 2 where e is a complex vector describing the polarization, set e = 1. ε () t is the envelope, which is real. Choose the unwinding phase: New base ket: iζ n () t ' n >= e n> E1 t ζ1() t = ; ζ () t = ωt+ ζ (); t 2 1

19 Riemann-Lebesgue lemma would directly lead to rotating wave approximation. Its physics significance is that if something oscillates too fast then its contribution is negligible. Note the criterion for the RWA to be valid. t t 1 1 2iωt µ () t C2() t dt () t C2() t e dt C 2 2 1( t) C1(0) ε + µ + ε t t t C2( t) = C2 (0) + i 1 * 1 * 2iωt µ ε () t C1() t dt C2() t dt µ + ε() t C2() t e dt where = E2 E1 ω; µ µ µ µ * + = 12 e, = 12 e ; Rotating Wave Approximation: RWA

20 After RWA i d dt 1 0 () t C Ω 1 2 C1 C = 2 1 C 2 Ω() t 2 with Rabi frequency : Ω ( t) = ε ( t) µ * µ = µ e 12

21 Adiabatic States Instantaneous energy eigenstate of a time-dependent Hamiltonian. 1 0 Ω() t 2 1 Ω() t 2 Ω + Ω + :" energy" Ω Ω Ω + :" energy" 2 2 Ω

22 Adiabatic Following When the energy separation between different adiabatic states are large enough, if the system is at a certain adiabatic state, i.e. pseudo-energy eigenstate, then it remains at this adiabatic state all the time. Adiabatic following requires Adiabatic Condition!

23 To understand STIRAP through Adiabatic States 3 LEVEL SYSTEM IS INDEED VERY SPECIAL COMPARED TO MULTI- LEVEL 1 0 Ω p () t Ωp() t p Ωs() t Ωs() t p s 2

24 Time Evolution of Adiabatic States p p s 1 0 Ω p () t Ωp() t p Ωs() t Ωs() t p s p p s t = - t = + Energy Eigenstates: 1>, 2>, 3> Adiabatic States, or fake energy eigenstates +>, 0>, -> Energy Eigenstates: 1>, 2>, 3>

25 The whole idea of STIRAP is: To choose a adiabatic state which coincides with the ground state at the very beginning, and corresponds to the desired final state at the very end. Or, even better Try to find an adiabatic state which is only the combination of initial and final level.

26 Can you have such a nice adiabatic state in Multilevel system? Hamiltonian of a multi-level system after RWA, when trying to construct a good adiabatic state: 2 0 Ω1, x x 1, , Ω Ω 0 Ω2, = λ N 1 Ω N 1, N ΩN 1, N 0 y y

27 Can you have such a nice adiabatic state in Multilevel system? If you have more than 3 level, this is the equation: Ω x = 1,2 N 1, N 0; Ω y = 0; You may still have STIRAP-like transitions in a multi-level system; the purpose is to involve as few intermediate states as possible.

28 Now, a closer look at 3 level STIRAP Adiabatic states: +>= sinθsin ϕ 1 >+ cos ϕ 2 >+ cosθsin ϕ 3 > 0 >= cos θ 1 > sin θ 3 > >= sinθ cos ϕ 1 > sin ϕ 2 >+ cosθ cos ϕ 3 > where the mixing angles are : tanθ =Ω ()/ t Ω () t p s 1 0 Ω p () t H = Ωp() t Ωs() t Ωs () t 0 2 ϕ = Ω t +Ω 2 2 tan 2 p( ) s( t)/

29 Now, a closer look at 3 level STIRAP Time evolution: () () 0 2 s s t t Ω Ω 1 0 () () () () 0 2 p p s s t t t t Ω Ω Ω Ω 1 0 () () p p t t Ω Ω 0 cos 1 sin 3 θ θ >= > > t = - t = + intermediate 1> 0> 3>

30 Adiabatic Condition & Requirements on Rabi Frequency Adiabatic Condition: we want adiabatic states to be far away enough from each other. ΩT >> 1 where T is the interaction time. To ensure the adiabatic following, we also want to match the Rabi frequency of the red and the blue light, i.e. make the shape and max value of those two the same.

31 Now, a closer look at 3 level STIRAP If we take the spontaneous emission into consideration: 1 0 Ω p () t H = Ωp() t iγ2 Ωs() t Ωs () t Γ i 3 2 A more suitable approach would be to describe the system via density matrix and consider the timeevolution of the density matrix. Yet calculations show that for our purpose these two methods yield the same result.

32 Numerical Results

33 I have not talked about detuning yet STIRAP is very robust against detuning of either light once the energy conservation is satisfied. Result for blue light detuning: The Y-axis is efficiency, the X- axis is detuning in MHz.

34 Our Vacuum System ~ 140cm

35 Our Vacuum System

36 Our Vacuum System

37 Our Vacuum System

38 Our Vacuum System

39 Our Experiment Amplification circuit DC voltage Scan of electric field Ramp voltage

40 A micro-channel plate (MCP) is a planar component used for detection of particles (electrons or ions) and impinging radiation ( ultraviolet radiation and X-rays). It is closely related to an electron multiplier, as both intensify single particles or photons by the multiplication of electrons via secon dary emission. It can additionally provide spatial resolution. Skematic Drawing from Wiki Micro Channel Plate: Ion Detector

41 Our Experiment

42 Scanning the Electric Field: Stark Effect E (V/cm) Energy levels of He Triplet states in an electric field

43 Transition Strength of Different Stark States By courtesy of Thomas H. Bergeman

44 Experimental Data on Stark States

45 Metastable Helium Energy Level Revisited

46 Measuring the Efficiency: Apply a third laser For those in Rydberg State For those not excited The 1083 nm light does not cause any coherent transition such that there is no momentum transfer. No mechanical effect They are in the metastable ground state hence sees the 1083 nm light. Momentum is transferred. They get pushed!

47 Curved Wave Front of 1083nm light When a atom gets kicked, its momentum is no longer in the same direction as the previous instant. Henceforth you can not achieve a larger kick by a wider laser beam. Here is what you do. You apply a lens and then you have curved wavefront. By carefully matching the curvature, you can see a big push on the atoms.

48 Our Experiment Aperture: 0.5mm(h)* 0.3mm (w) Deflected residual He* atoms Measured by SSD detector ~ 6mm 2300V 2cm He* beam 1070±230m/ 1083nm s 796nm 389nm ~23cm ~26cm ~140cm ~0.4cm MCP Phosphor screen

49 SSD: Stainless Steel Detector

50 SSD: Stainless Steel Detector Current Readings of SSD & the Beam Profile of the source

51 Our Experiment

52

53 Efficiency result

54 Efficiency Result

55 Intuitive Vs. Counter Intuitive 0.7mm (FWHM) 2.3mm 3.0mm 0.5mm He* beam 1070m/sblue mirror is on stage Normal Vs. STIRAP: Ion signal Rabi Frequency (MHZ) time (microseconds)

56 Ti-sapphire laser Titanium-sapphire refers to the lasing medium, a crystal of sapphire (Al2O3) that is doped with titanium ions. A Ti:sapph laser is usually pumped with another laser with a wavelength of 514 to 532 nm, for which argon-ion lasers (514.5 nm) and frequencydoubled Nd:YAG, Nd:YLF, and Nd:YVO lasers ( nm) are used. Ti:sapphire lasers operate most efficiently at wavelengths near 800 nm.

57 Ti-sapphire laser Absorption and emission cross sections for Ti:sapphire

58 Ti-sapphire laser Design of Standingwave and Ring resonators

59 Pound- Drever- Hall(PDH) Locking The Red Light: System Overview

60 Stabilization Scheme: Control Theory & Error Signal The concept of the feedback loop to control the dynamic behavior of the system: this is negative feedback, because the sensed value is subtracted from the desired value to create the error signal which is amplified by the controller.

61 PDH locking offers one possible solution to the wandering of laser frequency by actively tuning the laser to match the resonance condition of a stable reference cavity. Skematic Drawing from Wiki Pound Drever Hall Locking System

62 Locking laser to a Fabry-Perot cavity Transmission of a Fabry Perot cavity vs frequency of the incident light. This cavity has a fairly low finesse, about 12, to make the structure of the transmission lines easy to see. *Cited from: E. D. Black, An introduction to Pound Drever Hall laser frequency stabilization The reflected light intensity from a Fabry Perot cavity as a functionof laser frequency, near resonance. If you modulate the laser frequency, youcan tell which side of resonance you are on by how the reflected power changes.

63 Reflection F: F( ω) = ω r(exp( i ) 1) υ fsr ω υ 2 1 r exp( i ) fsr Where r is the reflection coefficient of the mirror *Cited from: E. D. Black, An introduction to Pound Drever Hall laser frequency stabilization Reflection of a monochromatic beam from a Fabry Perot cavity

64 PDH: Sideband Generation We apply an EOM(Electro-optic modulator) to generate two side bands: E inc = Ee 0 i( ωt+ βsin Ωt) E [ J ( β) + 2 ij ( β) sin Ω t] e = Ε [ J ( β) e + J ( β) e J ( β) e ] iωt iωt i( ω+ω) t i( ω Ω) t If the modulation amplitude β is very small compared to 1, then these 3 components almost contain all the original power.

65 PDH: Sideband Generation Reflection fro the F-P cavity: E = E [ F( ω) J ( β) e + F( ω+ω) J ( β) e ref iωt i( ω+ω) t F ω Ω J β e i( ω Ω) t ( ) 1( ) ] P = P F ω + P F ω+ω + F ω Ω ref c ( ) s{ ( ) ( ) } + PP F ω F ω+ Ω F ω F ω Ω Ωt * * 2 c s{re[ ( ) ( ) ( ) ( )]cos + F ω F ω+ Ω F * ( ω) F( ω Ω)]sin Ωt} * Im[ ( ) ( ) + { terms oscillating faster than 2 Ω}

66 PDH: Measuring the Error Signal When the carrier is near resonance and the modulation frequency is high enough that the sidebands are not: F( ω ±Ω) 1 F F +Ω F F Ω i F * * ( ω) ( ω ) ( ω) ( ω ) 2Im{ ( ω)} Only the sin term in the previous slide survives; Use a mixer to measure it.

67 PDH: Measuring the Error Signal The error signal: ε = ω ω+ω ω ω Ω * * 2 PP c s Im{ F( ) F ( ) F ( ) F( )} The Pound Drever Hall error signal, when the modulation frequency is high. Here, the modulation frequency is about 20 linewidths: roughly 4% of a free spectral range, with a cavity finesse of 500.

68 Our PDH System

69 Blue Laser 389 nm Saturation Absorption Spectroscopy Frequency Doubling Cavity

70 Frequency Doubling Cavity

71 Frequency Doubling Cavity

72 SAS Locking SAS: Saturation Absorption Spectroscopy

73 References: K. Bergmann et, al. Coherent manipulation of atoms and molecules by sequential laser pulses, K. Bergmann et, al. Advances in Atomic, Molecular, and Optical Physics, Vol 46 (2001). Xiaoxu Lu, Yuan Sun, H. Metcalf. Absolute Measurement of STIRAP Efficiency, DMAOP T. Cubel et, al. Coherent population transfer of ground-state atoms into Rydberg states PHYSICAL REVIEW A 72, (2005). J. Martin, B. W. Shore, and K. Bergmann. Coherent population transfer in multilevel systems with magnetic sublevels. III. Experimental results, PHYSICAL REVIEW A, VOLUME 54, NUMBER 2, F.T. Hioe and J.H. Eberly, Phys. Rev. Lett. 47, 838(1981). M.L.Zimmerman, M.G.Littman, M.M.Kash, Daniel Kleppner, Stark structure of the Rydberg states of alkali-metal atoms, Physical Review A, 20(6), 2251 (1979).

74 Thank You!