schmiegelow, walz, plenio, jelezko, calarco, jamieson, blattqiqfgba.df.uba.ar/giambiagi2019/ba...
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![Page 1: Schmiegelow, Walz, Plenio, Jelezko, Calarco, Jamieson, Blattqiqfgba.df.uba.ar/giambiagi2019/BA school FSK 4.pdf · 4-stroke engine cycle Harmonic trap potential ω =2π 1.4 MHz Ca+](https://reader033.vdocuments.co/reader033/viewer/2022042809/5f9393983784811db914fc49/html5/thumbnails/1.jpg)
The team
www.quantenbit.de
S. Wolf
V. Kaushal
K. Groot-B.
A Pfister
M. Müller
Y. Hermann
J. Vogel
F. Stopp
M. Werner
A.Müller
W. Li
L. Ortiz
J. Welzel
A. Bahrami
U. Poschinger
A Mokhberi
B. Lekitsch
H. Lehec
A.Conta
M. Salz
J. Schulz
J. Hilder
A. Stahl
Folman, Retzker, Wrachtrup, Meijer, Lesanowski, Hennrich, Zanthier, Lutz, Budker,
Schmiegelow, Walz, Plenio, Jelezko, Calarco, Jamieson, Blatt
BMBF QLinkX
DFG-FOR 2724
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• Introduction to ion trapping and cooling
• Trapped ions as qubits for quantum computing and simulation
• Implanting single ions for a solid state quantum device
• Rydberg excitations for fast entangling operations
• Quantum thermodynamics, heat engines, phase transitions
Mainz, Germany: 40Ca+
Quantum optics and information
with trapped ions
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Thermodynamics overview
Large system:
Many degrees of freedom
and many particles
Small system:
few degrees of freedom
and single particle
Quantum system:
Quantized degrees of freedom,
superpositions and entanglement
Average values
Thermal fluctuations
Brownian motion
Observation of
system matters
Probabilistic nature
of quantum processes
Work probability distribution
In equilibrium,
or at least very close to it
Correlations with
environment matter
Fluctuation theorems
Non-classical baths
Fluctuations unimportant
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Sadi Carnot
James Watt
Robert Mayer
heat heatHeat
Engine
mechanical
work
coldhot
Convert thermal
energy into
mechanical work
PISTON
RESERVOIR RESERVOIRSYSTEM
Classical heat engines
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• Single-ion Otto heat engine - classical operation
• Spin-driven single ion heat engine - quantum motion
• Autonomous heat engine – ticking regularly
• Vision of a multi-ion crystal quantum heat engine
• Defect formation in a structural phase transition
– universal Kibble Zureck scaling law
Structure of talk - trapped ion thermodynamics
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RF electrodes
in tapered geometry
Distance ion – endcaps: 4mm
Distance ion – electrodes: 1.5mm
RF driving: 1000Vpp at 30MHz
Axial trap frequency: 35kHz
Radial trap frequency: 6MHz
Setup of single ion heat engine
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heating
r
zF• Radial heating
• Axial equilibrium
position shifted
• Radial cooling
• Axial position
shifted back
Scheme of operation – single ion heat engine
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A
BC
D
Working cycle
heating
moving
cooling
moving
Driving resonantly
with axial trap freq.
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Princeton Instruments ICCD:
• 8 ns gate time
• 10 MHz frame reate
Stroboscopic motion measurements
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• Continuously: laser cooling
• At alternating times:
additional electric noise in
radial direction
Thermal radial excitation
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Stroboscopic thermometry by EIT
Peters, Wittrock, Blatt, Halfmann,
PRA 85, 063416 (2012)
Roos et al., Phys. Rev.
Lett. 85, 5547 (2000)
• Sensing ion motion
in ∆k-direction from
the scattered
intensity
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9mK
3mK
46mK
Stroboscopic thermometry by EIT
Roßnagel, et al, "Fast thermometry for trapped ions
using dark resonances", NJP 17, 045004 (2015).
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Working principle and results
Fully classical regime
P = 3.4 × 10–22 J/sη = 0.28% Roßnagel, et al, "A single-atom heat
engine", Science 352, 325 (2016)
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Power versus temperature difference
P = 3.4 × 10–22 J/sη = 0.28%
Roßnagel, et al, Sci.
352, 325 (2016)
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Spin-driven heat engine coupled to harmonic-
oscillator flywheel
Generic heat engine Implementation with 40Ca+ ion
Working medium Spin of the valence electron: ȁ↑ , ȁ↓
Thermal baths Controlling the spin by optical pumping
Gearing mechanism Spin-dependent optical dipole force
Storage for delivered
work
Axial oscillation: ȁ0 , ȁ1 , ȁ2 ,…
arXiv:1808.02390
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Spins Thermodynamics
𝑝↑ =1
1 + exp ℏ𝜔𝐿/𝑘𝐵𝑇𝜌 = 𝑝↑ ȁ↑ ۦ ȁ↑ + (1 − 𝑝↑)ȁ↓ ۦ ȁ↓
ȁ↓
ȁ↑
Thermal state Spin temperature
at 2𝜋 ∙ 13 MHz Zeeman splitting
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ȁ↓
ȁ↑
Cold bath: optical pumping
Warm bath: depolarising
ȁ↓
ȁ↑
Function Cooling Heating
Polarisation circular linear
Duration 180 ns 130 ns
Excitation (𝑝↑) 0.545(2) 0.828(3)
Temperature 0.4 mK 3.5 mK
Period ( = axial oscillation) 740 ns
S1/2
ȁ↑
P1/2
ȁ↓
𝜋
S1/2
ȁ↑
P1/2
ȁ↓
𝜎−
Controlling the Spins Thermodynamics
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4-stroke engine cycle
Harmonic trap potential
ω =2π 1.4 MHz Ca+ Ion
Spin 1/2
Pump laser: Polarization
alternating at ω
Spin-
dependend
force
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Heat-Engine setup
19
ΔS=
2π
2.7
MH
z
Harmonic trap potential
ω =2π 1.4 MHz Ca+ Ion
Spin 1/2
Lin ┴ lin optical lattice:
Alternating, spin-dependent Stark shift
λ = 280 nm
Pump laser: Polarization
alternating at ω
Schmiegelow et al., PRL
116, 033002 (2016)
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Heat-Engine protocol
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Heat-Engine protocol and readout of flyweel
Q function: ground statepopulation after displacement α
Measurement:1. Perform spin independent voltage kick D2. Robust population transfer for via rapid adiabatic passage on red sideband3. Detect spin {↑,↓}
Dingshun Lv et al., PRA 95, 043813 (2017)
S. An et al., Nature Phys. 11, 193 (2015)
arXiv:1808.02390
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Measured Q-function
Q function after 0, 6, 12, 18µs heat engine operation
Model Q function bydisplaced, squeezed thermal states (DSTS):
Reveal: for engine time tHE
arXiv:1808.02390
John Goold(Trinity, Dublin)
Mark Mitchison(Trinity)
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Outcome
arXiv:1808.02390
Mean energy
Ergotropy
Ergotropy: dominated by coh.
displacement β, withadd. contributionfrom squeezing ζ
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Optical pumping rates to emulate temperatures
Product state: scattered photonsin HE process destroyquantum correlationsspin - flyweel motion
Model
Master equ.
arXiv:1808.02390
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• Remove alternating pumping beam• Add resonant lattice with alternating polarization• „Temperature gradient“ should lead to self-excitation
Future extension: autonomous spin-driven engine
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Autonomous clock-work proposal
… laws of thermodynamics dictate a trade-off between the amount of dissipated heat and the clock’s performance in terms of its accuracy and resolution…
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Autonomous clock-work proposal
… laws of thermodynamics dictate a trade-off between the amount of dissipated heat and the clock’s performance in terms of its accuracy and resolution…
Vahala et al., Nat.
Phys. 5, 682 (2009)
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• Blue- and red-detuned beams near-resonant beams autonomous harmonic motion
• Damping and excitation balance• Doppler shift resonance at separate times
2ω periodicity in photon emission rates• Observe regular photons counting• Reveal phase stability
Phonon laser Vahala et al., Nat.
Phys. 5, 682 (2009)
Wagner et al, in preparation
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Oscillation amplitude
Cyc
le-a
vera
ged
scat
teri
ng
rate
s
Operating point
damping
excitation
Stable oscillation:
Scattering rates:
Random recoils
Stable operating point in oscillation Vahala et al., Nat.
Phys. 5, 682 (2009)
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Ion oscillates
Modulated signal
at detector
Scattering rate is
modulated
Oscillation Detection
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Stability analysis of clockwork
• Record photon klicks
• analyze their Allan variance
• Vary laser power of Cooling/heating
• Connection between
scat. rate (heat consumption / entropy increase) and
oscillator phase stability ?
Does thermodynamics
limit our ability to
measure time?
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Ion crystal:
• Implement multi-ion spin-driven engines
• Fully controlled ancilla-bath, non-Markowian
• Quantum entanglement in heat engines
• Interconnection between quantum error correction, quantum
computing and heat engines
future goals: multi-ion machines / reservoirs
Ancilla ions System ionsReservoir
Ancilla ionsReservoir
DFG-FOR 2724
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Observation of the Kibble Zurek scaling law
for defect formation in ion crystals
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1976 (Kibble)
symmetry breaking at a second order
phase transitions such that topological
defects form, this may explain formation of
cosmic strings or domain walls Thomas Kibble
(Imperial London)
Universal principles of defect formation
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1976 (Kibble)
symmetry breaking at a second order
phase transitions such that topological
defects form, this may explain formation of
cosmic strings or domain walls Thomas Kibble
(Imperial London)
Universal principles of defect formation
Free energy landscape changes
across the critical point from a single
well to a double well potential
Spontaneous symmetry breaking
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Universal principles of defect formation
• System response time, thus information transfer,
diverges when approaching critical point
• At some moment, the system becomes non-
adiabatic and freezes
Defines typ.
defect size
Linear quench
Diverging slow
response
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1976 (Kibble)
symmetry breaking at a second order
phase transitions such that topological
defects form, this may explain formation of
cosmic strings or domain wallsW. Zurek
(los Alamos)
Universal principles of defect formation
1985 (Zurek)
Sudden quench though the critical point leads to
defect formation, experiments in solid state phys.
may test theory of universal scaling
• Experiments with rapid cooling of liquid
crystals observe structures
• Experiments for vortex formation in liquid 3He
• Experiments with vortexes in superconductors
2010 (Morigi, Retzger, Plenio et al)
Proposal for KZ study in trapped ions crystals
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Germany before the structural phase transition
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Berlin at the critical point of the structural phase transition
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Germany after the structural phase transition
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Proposal for KZ physics with ion crystal
• Landau Ginzburg theory of phase transition for ion trap situation
• Universal scaling found
• Prediction of for the inhomogenious case
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Defect formation in ion crystals
Linear
Zig-zag
Zag-zig
Defect
Defect
Double defect
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Structural configuration change in ion crystals
Linear
Zigzag Zagzig
slow
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Linear
fast
Zigzag Zagzig
Defects
Structural configuration change in ion crystals
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Experimental setup
and parameters
• Trap with 11 segments
• Controlled by FPGA and arbitray
waveform gen.
/2 = 1.4MHz (rad.)
/2 = 160 – 250kHz (ax.)
• Laser cooling /
• CCD observation
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Smooth axial compression over critical point
• Exponential soft start and stop
• Low excitation of axial breathing mode
• Slope at critical point variable for variable quench times
• Acurate frequency determination
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Molecular dynamics simulations
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Molecular dynamics simulationsSimulation of
ion trajectories
Tiny axial
excitation
No position
flips
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Experimental test of the =8/3 power law scaling
Saturation of
defect density
Offset kink
formation
Saturation of
defect density
Offset kink
formation
= 2.68 ± 0.06, fits prediction
for inhomogenious Kibble
Zurek case with 8/3 = 2.66
Pyka et al, Nat.Com. 4, 2291 (2013)
Ejtemaee, PRA 87, 051401 (2013)
Ulm et al, Nat. Com. 4, 2290 (2013)
DelCampo, Zurek
arXiv:1310.1600
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Experimental test of the =8/3 power law scaling
Saturation of
defect density
Offset kink
formation
Saturation of
defect density
Offset kink
formation
Pyka et al, Nat. Com. 4, 2291 (2013)
Ejtemaee, PRA 87, 051401 (2013)
Ulm et al, Nat. Com. 4, 2290 (2013)
DelCampo,
Zurek, Int. J. Mod.
Phys. A 29,
1430018 (2014)
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Universal trapped-ionQuantum Computer
PRL 119, 150503
PRX 7, 031050
PRX 7, 041061
Single ions delivered for solid state QC
PRL 117, 043001
arXiv:1902.05308
Modern Quantum technologies
with trapped ions
F. Schmidt-Kaler
Sci. 352, 325
arXiv:1808.02390
PRL 115, 173001
arXiv:1905:05111
Rydberg ions
Nat.Com. 7, 12998
PRL 119, 253203
JOSA B 36, 565
Exotic ions: H+ / Th+
Ion heat engines
Transfer of optical OAMto a bound electron
PRA 99, 023420