Bloch oscillations in a cavity and spin-dependent kicks · Bloch oscillations in a cavity and...
Transcript of Bloch oscillations in a cavity and spin-dependent kicks · Bloch oscillations in a cavity and...
Bloch oscillations in a cavity and spin-dependent kicks
Paul HamiltonUniversity of California –
Los Angeles (UCLA)
T ∝ 1/Fz
𝐹𝐹𝑧𝑧
Hybrid trapsMolecular ions
Th nuclear clock
Cavity BlochMode-locked laser cooling
Mode-locked QC
Ion gyroscope
Radioactive qubits
Credit: ALMA(ESO/NAOJ/NRAO)
Interstellar chemistry
Search for sterile neutrinos
Paul Hamilton
Eric Hudson
UCLA AMO
138Ba+
OutlineOutline
1. Splitting the beamsplitter –
spin-dependent kicks (SDKs)1
2. Cavity based detection of Bloch
oscillations
1M. Jaffe, V. Xu, P. Haslinger, H. Müller, and P. Hamilton, Phys. Rev. Lett. 121, 040402 (2018).
Raman interferometry
Two ways to increase sensitivity: increasing T (space!) and increasing k
Δ𝜙𝜙 = −1ℏ�𝐿𝐿 𝑑𝑑𝑑𝑑 + Δ𝜙𝜙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙
= 𝑘𝑘 ⋅ �⃗�𝑎 𝑇𝑇2
Technical advantages
⟩|𝐴𝐴,𝑝𝑝 = 0
�|𝐵𝐵,2ℏ𝑘𝑘𝑙𝑙𝑒𝑒𝑒𝑒
Raman
ℏ𝜔𝜔1 ℏ𝜔𝜔2
Hyperfine 𝜔𝜔1 − 𝜔𝜔2 ≈ GHz
⟩|𝐴𝐴,𝑝𝑝 = 0�|𝐴𝐴,2ℏ𝑘𝑘𝑙𝑙𝑒𝑒𝑒𝑒)
ℏ𝜔𝜔1 ℏ𝜔𝜔2
Recoil frequency𝜔𝜔1 − 𝜔𝜔2 ≈ kHz
Bragg
Raman Bragg
Detection X
Velocity acceptance X
Systematics X
Momentum X
Laser power X
Can we get the best of both techniques?
Simpler detection and lower power requirements
Raman transitions
| ⟩𝐴𝐴,𝑝𝑝 | ⟩𝐵𝐵,𝑝𝑝+2ℏ𝑘𝑘
E
zt
𝜋𝜋 pulse𝜋𝜋/2 “beamsplitter”
Raman transitions
| ⟩𝐴𝐴,𝑝𝑝 | ⟩𝐵𝐵,𝑝𝑝+2ℏ𝑘𝑘
E
zt
𝜋𝜋 pulse
Spin-dependent kick (SDK)
| ⟩𝐴𝐴,𝑝𝑝 | ⟩𝐵𝐵,𝑝𝑝
E
zt
Optical Raman 𝜋𝜋 pulseMicrowave 𝜋𝜋/2 pulse
| ⟩𝐵𝐵,𝑝𝑝+2ℏ𝑘𝑘| ⟩𝐴𝐴,𝑝𝑝−2ℏ𝑘𝑘
Simple SDK inteferometer
Advantages
• Double the momentum splitting• State labelling • All optical pulses are 𝜋𝜋 pulses enabling use of ARP• AC Stark shift suppression
MW𝜋𝜋/2
MW𝜋𝜋/2
𝜋𝜋 𝜋𝜋𝜋𝜋 𝜋𝜋
• Adiabatic: “Slowly enough” change between two states
• Pop. transfer does not depend on: – Laser intensity– Interaction time(vs. π/2 or π pulses)
• This implementation:
– Scan laser frequency across Raman resonance
– Laser power: – 96% efficiency per pulse
(99% efficiency per ħk)
[1] Bruce W. Shore, Adv. Opt. Photon. 9, 563-719 (2017).
time
[1]
Gaussian beam (600 µm waist)
Atom cloud 350 µm
OutlineAdiabatic passage & efficiency
Adiabatic rapid passage (ARP)
Detuning (kHz)
Adiabatic rapid passage (ARP) can be used to increase the efficiency and bandwidth of the optical 𝜋𝜋 pulses.
Exci
tatio
n fra
ctio
n
After 1 ARP pulse
After 12 ARP pulses
1. Create superposition of hyperfine ground states
2. Adiabatic passage Raman transition, ±2ħk momentum (Ô±)– Repeat to increase momentum– Reverse to overlap atoms
3. Cavity and Doppler shift allows reversal of kick direction (could also use MW)
Benefit: If kicks are efficient, can do many to increase momentum transfer
OutlineSpin-dependent kicks for interferometry
Enabled by efficient kicks:
• Split a single atom source into two interferometers
• Enables measurement if phase shift between interferometers, typically for gravity gradiometry
• ~2 mm separation (phase shift externally induced by AC Stark shift)
OutlineRaman gradiometer
• Multi-loop interferometers• Sign of force sensitivity
alternates each loop• Single loop interferometer
averages out AC signal• Resonant interferometer
switches sign during each cycle– Averages out constants
(DC)– “lock-in” detection at
loop frequency
Journal club 10/10/2018 15
Outline“Juggling” interferometer
Prepare qubit superposition at center
+
Displace trapSpin dependent kicks (SDKs)OrbitRotate & Interfere
Ω
Trapped ion interferometry
Ion interferometer forrotation sensing
Parameters• 100 SDKs demonstrated (Monroe)• 100 𝜇𝜇m trap displacement• One Ba+ ion using Zeeman qubit
states• Sensitivity ~10−6 rad
s/ Hz
W C Campbell and P Hamilton 2017 J. Phys. B: At. Mol. Opt. Phys. 50 064002
Honeywell GG1320AN
SDK beams
Electrodes
Kicked ion
• SDK (spin-dependent kick) laser10 ps pulses, 80 MHz, 36 W avg power
• Ions will barely move during the picosecond pulses, leading to high fidelity.• Average acceleration of over 100,000 g quickly separates wavepackets.• Large bandwidth will allow use of thermal ions.• Could increase sensitivity of truly thermal neutral atom interferometers as
well..
Zeeman SDKs
Current status
• Raman transition driven usingpulse train
• Zeeman shift set to multiple oflaser repetition rate
• 𝜋𝜋2− 𝜋𝜋
2Ramsey sequence
demonstrated with co-propagating beams
OutlineOutline
1. Splitting the beamsplitter – spin-
dependent kicks (SDKs)
2. Cavity based detection of Bloch
oscillations
Atomic fountain force sensors
• Traditional matter wave interferometers: atoms act as test masses for force sensing.
• Roughly think about a potential difference across the arms leads to a phase shift.
Time0 T 2T
Hei
ght
Berkeley dark energy search
• Metal sphere creates gradient in scalar field
• Atoms act as test masses for force sensing
Time0 T 2T
Hei
ght
Results
=
=
Search for an anomalous acceleration when atoms are near the source
Limits on anomalous forces
aanomaly < 45 nm/s2 (95% confidence)
100x improvement on chameleon and symmetron bounds
Take home message: a few orders of magnitude more will either discover or rule out these theories
M. Jaffe, P. Haslinger, V. Xu, P. Hamilton, A. Upadhye, B. Elder, J. Khoury, and H. Müller, Nature Physics 13, 938 (2017).
Simple CW atom interferometer
“Ideal” atom interferometer:
• Simple
• Compact
• High sensitivity
• Continuous measurement
Goal: Turn on a laser and plug the output of a detector into an oscilloscope.
Enable measurement of AC signals
Principle: Monitor atoms effect on a standing wave in an optical cavity
Continuous trapped accelerometer
Adapted from Peden et al.Phys. Rev. A 80, 043803 (2009)
T ∝ 1/Fz
𝐹𝐹𝑧𝑧
Atomic wavefunction modulates at Bloch frequency…
which couples to the intracavitylattice…
leading to modulation of the output light field.
Collectively couple atomic “wave” to the optical cavity.
Bloch oscillationsBloch theorem: Wavefunction of a particle in a periodic potential is
𝜓𝜓 𝑟𝑟 = 𝑒𝑒𝑖𝑖 𝑞𝑞 𝑙𝑙𝑢𝑢(𝑟𝑟)
where q is the “quasimomentum” in the potential and u(r) is a periodic function which repeats every lattice site.
Force on a particle in a periodic potential (Bloch 1928) causes the quasimomentum to change in time
𝑞𝑞 𝑡𝑡 = 𝑞𝑞0 + 𝐹𝐹𝑡𝑡and undergoes Bragg reflection at the edge of Brillouin zone.
Bloch oscillations
In quantum mechanics a force on a particle in a periodic potential leads to changes in momentum called Bloch oscillations.
𝜔𝜔𝐵𝐵𝑙𝑙𝐵𝐵𝐵𝐵𝐵 = 𝐹𝐹 × 𝜆𝜆2
/ℏ (~kHz scale)
Tino PRL 106, 038501 (2011)
Usual method:1. Bloch oscillations in lattice2. Release atoms3. Destructively image
Cavity Bloch theory
Numerical simulations
• 106 Yb atoms
• Bloch frequency 7.4 kHz
• Cavity – 5 cm long, 99.9%
reflectivity, 1 MHz linewidth
• Lattice depth 3 ER
• Collective cooperativity
>10,000
→ 10-7 g / √Hz
Testing dark energy
Dark energy
Projected 10−9𝑔𝑔 sensitivity in one day of integration
⇒ Rule out chameleons and constrain other scalar theories
• Reduced vibration sensitivity / easier isolation• Long coherence time
Model Description
Chameleon Mass couples to matter density
Symmetron Coupling depends on matter density
f(R) gravity Equivalent to chameleon theory
Preferred scale Maps to chameleon theory
OutlineDark matter candidates
XKCDUltra low mass fields coherently oscillating
For example: 1 kHz × ℎ = 10-12 eV
Testing dark matter
Dark matter
Time varying dilatons oscillate at Compton frequency.
10 kHz detection bandwidth for an EP test could improve constraints& Rb
Tilburg Phys. Rev. D 91, 015015
Current status• Zeeman slowed atoms captured directly
in intercombination line MOT.
• ~105 atoms loaded into lattice
• Coupling to cavity demonstrated
• Working on initializing Bloch oscillations
Thanks
Postdocs
Robert NiederriterAdam West
Graduate students
Chandler SchlupfRandy PutnamSami Khamis
Undergraduates
Kayla RodriguezYvette de Sereville
Collaborators
Eric Hudson (UCLA)Peter F. Smith (UCLA)Jeff Martoff (Temple)Andrew Renshaw (Houston)Peter Meyers (Princeton)Wes Campbell (UCLA)Holger Muller (Berkeley)