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

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

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.

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

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

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

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

Magnetic Traps Macro-Magnetic Traps: Micro-Magnetic Chip Traps: - Large currents in large coils. - Very deep, very stable traps. - dB/dx is small  ftrap ~ 10-100 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 ~ 0.1-1 kHz.

Magnetic Traps Macro-Magnetic Traps: Micro-Magnetic Chip Traps: - Large currents in large coils. - Very deep, very stable traps. - dB/dx is small  ftrap ~ 10-100 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 ~ 0.1-1 kHz. Spin Dependence: Vtrap ~ mF|B|  RF spin-flip evaporative cooling. Quantization B-field must be small .

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

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

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

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

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

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.

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.

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.

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.

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.

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.

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

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.

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

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

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

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.

 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)

 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)

 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)

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 !!!

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

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).

Potassium is easier than Rubidium 41K Hyperfine splitting = 254.0 MHz. Feshbach resonance @ ~51 G.  |F=1,mF=-1 39K Hyperfine splitting = 461.7 MHz. Feshbach resonance @ 402 G.  |F=1,mF=+1  Feshbach zero @ 350 G.

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

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)

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

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

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

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

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 !!!

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

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

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

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

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

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]

Recent Developments

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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, 241-249 (2006).

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

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!

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

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

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.

Spin-dependent Beamsplitter – Step 3 Magic BIoffe

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

Apparatus

Actual Progress

Actual Progress

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

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

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