1. RF and Microwave Near-Field Traps for Ultracold Atoms
Seth A. M. Aubin
Dept. of Physics, College of William and Mary
May 14, 2010
Universidad Autonoma de San Luis Potosi

2. Outline 1. A brief review of conservative traps
 What’s missing?
2. RF and Microwave traps
 Theory
 atom chip
3. Applications
 Interferometry
 Atomtronics
 Cooling

3. Conservative Traps Magnetic Traps Optical Dipole Trap
- Highly reliable.
- Near perfect potentials …low heating rates.
- Spin dependent … somewhat.
- Low magnetic field.
Optical Dipole Trap
- Reliable.
- Near perfect potentials
- Some heating.
- Spin independent … mostly.
- Arbitrary magnetic field  Feshbach resonances.

4. Magnetic Traps -- Review
Interaction of atomic magnetic moment with B-field: B 

5. Magnetic Traps -- Review
Interaction of atomic magnetic moment with B-field: B 

6. Magnetic Traps -- Review
Interaction of atomic magnetic moment with B-field: B 
For an atom in the hyperfine state

7. Magnetic Traps -- Review
Interaction of atomic magnetic moment with B-field: B 
For an atom in the hyperfine state
Energy = minimum
|B| = minimum

8. Magnetic Traps Macro-Magnetic Traps: Micro-Magnetic Chip Traps:
- Large currents in large coils.
- Very deep, very stable traps.
- dB/dx is small  ftrap ~ Hz.
N ~ 106, T ~ 100 K
Micro-Magnetic Chip Traps:
- A few Amps.
- Atoms trapped a few 100 m from thin wires.
- dB/dx is large  ftrap ~ kHz.

9. Magnetic Traps Macro-Magnetic Traps: Micro-Magnetic Chip Traps:
- Large currents in large coils.
- Very deep, very stable traps.
- dB/dx is small  ftrap ~ Hz.
N ~ 106, T ~ 100 K
Micro-Magnetic Chip Traps:
- A few Amps.
- Atoms trapped a few 100 m from thin wires.
- dB/dx is large  ftrap ~ kHz.
Spin Dependence: Vtrap ~ mF|B|
 RF spin-flip evaporative cooling.
Quantization B-field must be small

10. Optical Dipole Traps -- Review
cold 87Rb atoms in a dipole trap
[Havey group, Old Dominion University]

11. Optical Dipole Traps -- Review
2-level atom  E1
cold 87Rb atoms in a dipole trap
[Havey group, Old Dominion University]
AC Stark effect shifts the energy levels

12. Optical Dipole Traps -- Review
2-level atom  E1
cold 87Rb atoms in a dipole trap
[Havey group, Old Dominion University]
AC Stark effect shifts the energy levels

13. Optical Dipole Traps -- Review
2-level atom  E1
cold 87Rb atoms in a dipole trap
[Havey group, Old Dominion University]
AC Stark effect shifts the energy levels
Field
OFF ON
low-field
seeker
high-field
 < 0

14. Optical Dipole Traps -- Review
2-level atom  E1
cold 87Rb atoms in a dipole trap
[Havey group, Old Dominion University]
AC Stark effect shifts the energy levels
Field
OFF ON
low-field
seeker
high-field
 < 0
Field
OFF ON
low-field
seeker
high-field
 < 0

15. Red-detuned dipole traps
Laser Dipole Traps
Red-detuned dipole traps
atoms trapped in laser focus  Harmonic trap (nearly perfect).
Very large detunings (~100 nm) to limit heating.
Easy to make  widely used.

16. Red-detuned dipole traps Blue-detuned dipole traps
Laser Dipole Traps
Red-detuned dipole traps
atoms trapped in laser focus  Harmonic trap (nearly perfect).
Very large detunings (~100 nm) to limit heating.
Easy to make  widely used.
Blue-detuned dipole traps
atoms trapped in the dark  Square well trap.
Large detunings (~1-10 nm) to limit heating.
Difficult to make  specialty trap.

17. Red-detuned dipole traps Blue-detuned dipole traps
Laser Dipole Traps
Red-detuned dipole traps
atoms trapped in laser focus  Harmonic trap (nearly perfect).
Very large detunings (~100 nm) to limit heating.
Easy to make  widely used.
Blue-detuned dipole traps
atoms trapped in the dark  Square well trap.
Large detunings (~1-10 nm) to limit heating.
Difficult to make  specialty trap.
Spin-dependent in principle
At very large detuning  spin independent trapping.
Operate at arbitrary magnetic field  Feshbach resonances.

18. A better conservative trap
Wish List:
Qualitatively spin dependent.
Target qualitatively different potentials to different spin states.
Harmonic trapping … or other.
Low heating, low decoherence.
Operate at arbitrary magnetic field
 Feshbach resonance
 tune atom-atom interactions. …
Easy to make.
Low cost.

19. Applications Quantum gates: state-dependent logic gate.
Interferometry: spin-dependent interferometer.
Atomtronics:  spin-pumping
 spin transistor
Adiabatic-sympathetic cooling.
Single 1D trap with tunable atom-atom interactions.
 Tonks gas, Luttinger liquid.
 1D wire for atomtronics.

20. Applications Quantum gates: state-dependent logic gate.
Interferometry: spin-dependent interferometer.
Atomtronics:  spin-pumping
 spin transistor
Adiabatic-sympathetic cooling.
Single 1D trap with tunable atom-atom interactions.
 Tonks gas, Luttinger liquid.
 1D wire for atomtronics.

21. RF and Microwave Potentials
SOLUTION
RF and Microwave Potentials
IDEA:
Use the AC Zeeman effect.
Target hyperfine M1 transitions.

22. RF and Microwave Potentials
SOLUTION
RF and Microwave Potentials
IDEA:
Use the AC Zeeman effect.
Target hyperfine M1 transitions.
BENEFITS:
Easy physics !!!
No spontaneous emission.
RF and microwave M1 transitions  well established technology.
 spin dependent.
Physics works at all magnetic fields.

23. RF Theory Theory is simple  > 0  < 0  M1
Potential energy is similar to a laser dipole trap
Field
OFF ON
low-field
seeker
high-field
 > 0
Field
OFF ON
low-field
seeker
high-field
 < 0

24. RF Theory Theory is simple  > 0  < 0  M1
Potential energy is similar to a laser dipole trap
M1 transition amplitude
Field
OFF ON
low-field
seeker
high-field
 > 0
Field
OFF ON
low-field
seeker
high-field
 < 0

25. RF Theory Theory is simple  > 0  < 0  M1
Potential energy is similar to a laser dipole trap
M1 transition amplitude
Probability to be in the untrapped state
Field
OFF ON
low-field
seeker
high-field
 > 0
Field
OFF ON
low-field
seeker
high-field
 < 0

26. Some Considerations
The trap or potential will be operated with large quantization magnetic field (B > 1 Gauss).
Trapping potential is “vectorial”:
Trapping potential is naturally harmonic:
Spin-dependence  energy selectivity
 M1 selection rules
Either the |g or |e state can be used for trapping.

27.  Energy Selectivity & M1 Selection Rules
Spin-Dependence
[ 87Rb, 39K, 41K ]
Low Magnetic Field]
 Energy Selectivity & M1 Selection Rules
mF=+2
Energy
F=2
mF=+1
mF=0
mF=-1
mF=-2
mF=-1
mF=0
F=1
mF=+1
Fz quantum number (mF)

28.  Energy Selectivity & M1 Selection Rules
Spin-Dependence
[ 87Rb, 39K, 41K ]
Low Magnetic Field]
 Energy Selectivity & M1 Selection Rules
mF=+2
Energy
F=2
mF=+1
mF=0
mF=-1
mF=-2
 - polarized RF
BIoffe // BRF
mF=-1
mF=0
F=1
mF=+1
Fz quantum number (mF)

29.  Energy Selectivity & M1 Selection Rules
Spin-Dependence
[ 87Rb, 39K, 41K ]
Low Magnetic Field]
 Energy Selectivity & M1 Selection Rules
mF=+2
Energy
F=2
mF=+1
mF=0
mF=-1
mF=-2
 - polarized RF
BIoffe // BRF
 - polarized RF
BIoffe  BRF
mF=-1
mF=0
F=1
mF=+1
Fz quantum number (mF)

30. Also, RF optics seems hard !!!
… but  is too big !!!
300 MHz   = 1 m
3 GHz   = 10 cm
Gigantic RF intensities will be be necessary for sufficient gradient !!!
Also, RF optics seems hard !!!

31. NIST 1993 Build-up cavity. 1 kW of circulating power !!!
Trap frequency ~ 1-3 Hz.
Weaker than gravity !!!
Poor optical access.

32. RF Near-Fields on Atom Chips
SOLUTION
RF Near-Fields on Atom Chips
RF magnetic near-fields have same form as static B-field.
 NO wavelength dependence !!!
Use atom chip to generate RF near-field trapping potential.
 Large gradients easy to achieve at moderate power (<10 W).

33. Potassium is easier than Rubidium
41K
Hyperfine splitting = MHz.
Feshbach ~51 G.
 |F=1,mF=-1
39K
Hyperfine splitting = MHz.
Feshbach 402 G.
 |F=1,mF=+1
 Feshbach 350 G.

34. An RF trap design (I) Bext generated on chip.
Only magnetic minima can be created for near-fields.

35. An RF trap design (II) |F=1, mF=-1 trapped.
Target transition: |F=1, mF=-1  |F=2, mF=-2.
166 MHz (other allowed transitions at 35 MHz & 256 MHz).
Plots for  = 2  1 MHz, BIoffe= 51 G, IRF = 0.5 A (< 5 W).
Pother= 0.015%
100
200
Potential energy (K)
distance from chip (m)
Z (m)
X (m)

36. Transmission Line Design
Improved performance for RF and microwaves a
+ I / 2
+ I / 2 h
Atom Chip
- I

37. Transmission Line Design
Improved performance for RF and microwaves
RF Trap
a2/h a
+ I / 2
+ I / 2 h
Atom Chip
- I

38. Transmission Line Design
Improved performance for RF and microwaves
RF Trap
a2/h a
+ I / 2
+ I / 2 h
Atom Chip
- I

39. What about potential roughness ?
Atom chip traps have a lot of potential
… but they have been plagued by trap roughness.
T=7 K

40. What about potential roughness ?
Atom chip traps have a lot of potential
… but they have been plagued by trap roughness.
T=7 K
The vector nature of the RF potential suppresses the primary roughness mechanism !!!

41. RF vs. DC Potential Roughness
Top View
wire
imperfection
BIoffe I
Bwire

42. RF vs. DC Potential Roughness
Top View
wire
imperfection
BIoffe
B// = Bwiresin ~ Bwire  I
 <<<1
Bwire

43. RF vs. DC Potential Roughness
Top View
wire
imperfection
B = Bwirecos ~ Bwire (1-2)
BIoffe
B// = Bwiresin ~ Bwire  I
 <<<1
Bwire

44. RF vs. DC Potential Roughness
DC Trapping Potential
Top View
VDC ~ |BIoffe + Bwire|
wire
imperfection
B = Bwirecos ~ Bwire (1-2)
BIoffe
B// = Bwiresin ~ Bwire  I
 <<<1
Bwire

45. RF vs. DC Potential Roughness
DC Trapping Potential
Top View
RF Trapping Potential
VDC ~ |BIoffe + Bwire|
VRF ~ |Bwire(1- 2)|2
wire
imperfection
B = Bwirecos ~ Bwire (1-2)
BIoffe
B// = Bwiresin ~ Bwire  I
 <<<1
Bwire

46. RF vs. DC Potential Roughness Preliminary Simulations
Deviation from flat (K)
longitudinal axis (m)
1-2 order of magnitude suppression !!!
0.43 m “bump”
[DC and RF potentials have identical trapping frequencies]

47. Recent Developments

48. Outline 1. A brief review of conservative traps
 What’s missing?
2. RF and Microwave traps
 Theory
 atom chip
3. Applications
 Interferometry
 Atomtronics
 Cooling

49. Outline 1. A brief review of conservative traps
 What’s missing?
2. RF and Microwave traps
 Theory
 atom chip
3. Applications
 Interferometry
 Atomtronics
 Cooling

50. Boson vs. Fermion Interferometry
Bose-Einstein condensates
Photons (bosons)  87Rb (bosons)
Laser has all photons in same “spatial mode”/state.
BEC has all atoms in the same trap ground state.
Difficulty
Identical bosonic atoms interact through collisions.
 Good for evaporative cooling.
 Bad for phase stability: interaction potential energy depends on density -- phase is unstable.
Degenerate fermions
Ultra-cold identical fermions don’t interact.
 phase is independent of density !!!
Small/minor reduction in energy resolution since E ~ EF .
Equivalent to white light interferometry.

51. RF adiabatic potential
RF beamsplitter
How do you beamsplit ultra-cold atoms ?
RF adiabatic potential 
RF dipole potential x
Energy h

52. RF beamsplitter
How do you beamsplit ultra-cold atoms ? x
Energy h

53. RF beamsplitter
How do you beamsplit ultra-cold atoms ? x
Energy h

54. RF beamsplitter How do you beamsplit ultra-cold atoms ? Energyx
Energy
Position of well is determined by 
hrabi =
Atom-RF coupling h

55. figure from Schumm et al., Nature Physics 1, 57 (2005).
Implementation
figure from Schumm et al., Nature Physics 1, 57 (2005).

56. RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a final value
BRF ~ 1 Gauss

57. RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a final value
BRF ~ 1 Gauss

58. RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a final value
BRF ~ 1 Gauss

59. RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a final value
BRF ~ 1 Gauss

60. RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a final value
BRF ~ 1 Gauss

61. RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a final value
BRF ~ 1 Gauss

62. RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a final value
BRF ~ 1 Gauss

63. RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a final value
BRF ~ 1 Gauss

64. Interferometry Experiment
Fringe spacing = (h  TOF)/(mass  splitting)

65. Species-dependent Potentials
K40 probe (Rb87 present but unseen):
Rb87 probe (K40 present but unseen):
K40 +Rb87 probes (both species visible but apparent O.D. about 50% smaller than actual):
Atomic Physics 20, (2006).

66. The problem with fermions (I)
DFG beamsplitting
BEC beamsplitting
0 = 1 = … = N-1  interference fringes!
0 ≠ 1 ≠ … ≠ N-1  interference washed out!

67. The problem with fermions (II)
Beamsplitting process must not depend on external state of atoms.
0 = 1 = … = 9  interference fringes!
0 ≠ 1 ≠ … ≠ 9  interference washed out!

68. Trapped Fermion Beamsplitters
Idea: spin-dependent potential or force
Opposite spins experience same potential, but shifted in opposite directions

69. Spin-dependent Beamsplitter – Step 1
40K
(fermion)
Field
OFF ON
low-field
seeker
high-field
 < 0

70. Spin-dependent Beamsplitter – Step 2
100
200 5
atom-chip distance (m)
Potential (K)
RED wires produce a RF potential gradients.
BLACK wire produces a DC magnetic trap for both spin states.

71. Spin-dependent Beamsplitter – Step 3
Magic BIoffe

72. Casimir-Polder measurement ?
Spin-dependent beamsplitter advantage: arbitrarily small arm/spin separation.

73. Apparatus

74. Actual Progress

75. Actual Progress

76. Summary Reviewed Magnetic and Laser Dipole Traps.
Microwave and RF potentials.
Application to Fermion Interferometry.
Experimental apparatus.

77. Ultra-cold atoms group
Francesca Fornasini
Prof. Seth Aubin
Brian Richards
Austin Ziltz
Jim Field
Megan Ivory

78. Thywissen Group Staff/Faculty Postdoc Grad Student Undergraduate
Colors:
Thywissen Group
S. Aubin
B. Cieslak
L. J. LeBlanc
M. H. T. Extavour
J. H. Thywissen
D. McKay
S. Myrskog
A. Stummer
T. Schumm