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)