Stop thinking classically!

Thomas BuschQuantum Simulators

Thomas BuschMotivation
New physics always lead to more insight and new technologies

Classical Mechanics

Thermodynamics

Electrodynamics

Special/General Relativity(Newton ~1700)(Carnot ~1830)(Maxwell ~1850)(Einstein ~1915)

what about the physics of the really small?
Quantum Mechanics

Motivation
Quantum Mechanics(Bohr ~1920)

MRI scanners work on the spin of a particle (which are tiny magnets)

But these are many-particle quantum mechanical e ects
the world is too big and/or too hot and/or too slow to deal
with single particle QM e ects

until very recently...

ff

ff

The second quantum revolution: quantum computing, communication,
metrology, simulations,….

Brief Review of Progress

1023

number ofatoms inquantum systems
that are of interestand that can becontrolled

many-bodyquantum

fully controllable
many-particle systems

105

towards highly versatile quantum simulatorsconquering
Hilbert space
single
atom

1
time

recent pastnow

futurethe problem is that quantum systems are very fragile and the important coherences decay quicklyfineed to nd a good system

Ultracold Atoms
Synthetic 3D atomic structures assembled atom by atom 2017:

BEC 1995:

JILA 1995
CNRS 2017a gas of atoms at essentially zero temperature

2001

full control over all degrees of freedom

Ultracold Atoms for Engineering
painted potentials
artificial gauge fields

Feshbach resonances

dimensionality
Rydberg atoms

H = Hkinetic + Hpotential + Hinteractions
dipolar atoms
optical lattices
spin-orbit coupling

magnetic traps
atom chips

droplets

optical tweezers

Floquet engineeringspinor wavefunction | i
hybrid systems: interfacing
atoms and photons

internal statesby no means complete!

different species (bosons and fermions)atoms and molecules

cold atomic systems are highly controllable, versatile and can be measured in many ways
foreordained for exploring new quantum few/many body physics with large control

real systems are often hard to access and can be noisy or impure
use a highly con gurable quantum system to model the original system

Example: new materials that meet speci c requirements
classical computing is not powerful enough to predict relevant properties in systems with, for example, strong correlations

Example: Alzheimers, Parkinsons and Huntingtons diseases are caused by misfolded protein molecules
Quantum simulations can help understand protein folding and help cure these diseases.

Example: quantum for the environmentfi

fi

understanding the precise quantum dynamics of chemical reactions can bene ts our environment. Quantum simulators could
nd chemical catalysts to remove CO2 from the atmosphere, or reduce the massive amounts of energy needed to make fertilizers.

fi

fi

Ultracold Atoms for Quantum Simulations

Example: Optical Lattices
arrange single atoms in space; synthetic condensed matter systems

reduced complexity, reduced noisy, no imperfections etc.
super uid

Mott insulator

quantum
phasetransition

flbut quantum simulators can also help to get into new parameter regimes

Example: Arti cial Magnetic Fields
ultracold atoms are neutral, cannot be used to study the e ects of magnetic eldsbut, the e ects of external magnetic elds is for a particle to pick up a phase when moving around a closed trajectory

fi

ff

fi

fi

ff

ff

we can do that in di erent ways: same physics, new regimes

Quantum Simulators: Example
these are all very helpful new experiments, but also very simple simulators
quantum engineering toolbox is growing quickly, but to solve all problems new ideas need to be developed

Develop and idea is four easy steps:
1. Remember the optical lattice? Distance between two atoms is given by the optical wavelength (100s nm)
2. But what if we want the atoms to be closer together? Cannot be done with optical waves…
3. But, in quantum mechanics particles are waves (and waves are particles)
4. Can we use matter waves?

Quantum Phase Transition for interaction particles w/out a lattice?
Aim: Realise an insulator phase transition purely via BEC
atomic interactions
and without an externally imposed lattice potential. (effective 1D model)

TG gasimmerse a strongly interacting gas in a BEC (matter wave), imbalanced system

Noninteracting

uncoupled

coupledInteracting
BEC
BEC
stronglyinteractingTG
gas gasNoninteracting

interacting gas is a superfluid

Interacting

can the BEC act like a matter-wave lattice?
what determines the distance between the trapped atoms?
extension of many-body quantum simulator?

interacting gas is an insulator

8

Pinned StateT =0<latexit sha1_base64="vY1A9Zz7PBHcEgksXETGP1xh+Cs=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE1ItQ9OKxYr+gDWWz3bRLN5uwOxFK6E/w4kERr/4ib/4bt20OWn0w8Hhvhpl5QSKFQdf9cgorq2vrG8XN0tb2zu5eef+gZeJUM95ksYx1J6CGS6F4EwVK3kk0p1EgeTsY38789iPXRsSqgZOE+xEdKhEKRtFKD41rt1+uuFV3DvKXeDmpQI56v/zZG8QsjbhCJqkxXc9N0M+oRsEkn5Z6qeEJZWM65F1LFY248bP5qVNyYpUBCWNtSyGZqz8nMhoZM4kC2xlRHJllbyb+53VTDK/8TKgkRa7YYlGYSoIxmf1NBkJzhnJiCWVa2FsJG1FNGdp0SjYEb/nlv6R1VvUuqt79eaV2k8dRhCM4hlPw4BJqcAd1aAKDITzBC7w60nl23pz3RWvByWcO4Recj2+hk41f</latexit>

BEC (GPE):
N

immersed gas (exact):

numerically solve the coupled equations

adiabatically ramp gm

(a)
(a)
(a)

gm = 1

ggmm
1.5
gm
g==
0
=0 0
m=

gm
gm
g=
=1 1
m=1

8

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111

⇢(x)
⇢(x)
⇢(x)

⇢(x)

µ0 /gcµ0 /gcµ0 /gc

1
111
000
0.8
0.8
0.8
0.8
0.6
0.6
0.6
0.6
111
0.4
0.4
0.4
0.4
0.2
0.2
0.2
0.2
222
0
000
16
161616 8 8 8 x
0 0 0 8 8 8 161616 161616 8 8 8 0x
0 0 8 8 8 161616 161616 8 8 8 0 0x
0 8 8 8 161616
xxx||| (x)|

2
(x)|2
(x)|2

0
x

gm
gm
g=
=1.5
1.5
m=1.5

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102<latexit sha1_base64="8yaoKCskarkczxuKjVJDmOoaVJQ=">AAAB6HicbVBNS8NAEJ34WetX1aOXxSJ4KomIeix68diC/YA2lM120q7dbMLuRiyhv8CLB0W8+pO8+W/ctjlo64OBx3szzMwLEsG1cd1vZ2V1bX1js7BV3N7Z3dsvHRw2dZwqhg0Wi1i1A6pRcIkNw43AdqKQRoHAVjC6nfqtR1Sax/LejBP0IzqQPOSMGivVn3qlsltxZyDLxMtJGXLUeqWvbj9maYTSMEG17nhuYvyMKsOZwEmxm2pMKBvRAXYslTRC7WezQyfk1Cp9EsbKljRkpv6eyGik9TgKbGdEzVAvelPxP6+TmvDaz7hMUoOSzReFqSAmJtOvSZ8rZEaMLaFMcXsrYUOqKDM2m6INwVt8eZk0zyveZcWrX5SrN3kcBTiGEzgDD66gCndQgwYwQHiGV3hzHpwX5935mLeuOPnMEfyB8/kD6DGNAg==</latexit>

periodic arrangement of localised impurities
222
101010period is given by inverse Fermi momentum

Pinned State: e ective model

0
x

8

2
16

16

8

0

x

1
0.8
0.6
L
0.4
N
0.2
0
8
16
16

1
1
2 )e iµ̃t(x, t) =(µ̃ gm | (x)|
0.8
gc
0.6
0.4
0.2
effective model for single impurity
0
16
8 0
8
16
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8

0
x

8

16

102

1
(c)

r

E
pinned state density
Numerics
E⇡|

0

1

12

a2
pin
6

35
gm

2
a a |
3 0 pin4n

9 5

Numerics

gm = 2
gm = 010 4

13

1 (x) =

r

gm N
1+
g c Nc

0

1

2

10 4

3 into account4
5
takeenergyneeded to prevent TG atoms fromgm dispersing and required to displace BEC density
apin = a0

Aside: state looks and smells somehow like a boson FFLO state…

2
a0
1
g
10 1 with a0 = m
2 cosh (a0 x)
2gc

a2
2
E ⇡ | pina a state|
Soliton-like
6
3 0 pin<latexit sha1_base64="dn36dF0JkuOWrkLm96pPfQlFhoU=">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</latexit>

ff

13

10 1

E

En0

<latexit sha1_base64="eqKXJ69cqhxHyZMriLsygSSmoNU=">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</latexit>2µ̃ = µ0✓(c)0gm = 2
gm = 0<latexit sha1_base64="2XSEMGNP+arSTJwdquAVUlb83Ss=">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</latexit>

102

(b)

1

gm ⌧ µ0 L/N

E

8

1

BEC in gThomas-Fermi
regime form = 1.5

gm = 1⇢(x)µ0 /gc0| (x)|216

ggmm==1.5
0

⇢(x)

(a)

gm = 1<latexit sha1_base64="51uHj+5dbgl83Vntr4p+WJWJ3rE=">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</latexit>p

1 + 2✏✏

1

6a20< a0 with ✏ =5µ̃◆gm = 1

gm = 1.5

0

8

16

16

1

1

E

gm = 2
gm = 02
5

9

In the shifted reference frame:
0
E = EN+1

0
EN⇡ |E10 |

1
0.8
0.6
0.4
0.2
0

102
(c)

2
16

8

0 Numerics
816a2
E ⇡ | pin
6

1

0(b)

1

2

0

n

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1

13
En0

En0

0

gm = 016
160| (x)|2(b)

1

0 (a)8x

8µ0 /gc

8

3

16

8

0
x

2
a a |
3 0 pin

4

10 1
8

16

10
(c)
5

16

8

0

8

16

102

4

gm

1

E

Numerics

gm = 2
gm = 0

2
1

5

9

13

n

these are all results for zero temperature.

10 1

a2
E ⇡ | pin
6

0

1

2

3
gm

2
a a |
3 0 pin

4

5

10 4

E

| (x)|2

when2does the gap open?

⇢(x)

1

energy gap separates the pinned states from the continuum

16

1
0.8
0.6
0.4 model to estimate the size of the energy gap?
Can we use the effective
0.2
0=1
gm = 1.5
8 0
8 gm16⇢(x)µ0 /gcPinned State:phasetransition
0E

gm = 0ΔE(a)does the self-pinning state survive at finite temperature?

density of the Tonks-Girardeau gas at finite temperature:2| (x)| =1
Xn=1

fn | n (x)|

2

where

fn =

1
exp [ (Enµ)] + 1

with Fermi-Dirac distribution

fn | n (x)|

2

where

fn =

1
exp [ (Enx<latexit sha1_base64="r1iW3DcJevo8TrIM4vhMzDUPrVI=">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</latexit>

20

1

10

0.75

0

0.5

10

0.25

20

0

µ)] + 1and assuming that the temperature of the BEC does not change

initially a large energy gap protects the pinned stateparticles start to be ejected from the pinned state in a crossover region
at high temperature all particles are delocalisedfi1

Pinned State: nite temperature00.1

pinned

0.2
T /Tf

0.3

0.4

delocalised thermal statePinned State: nite temperature
modify the effective Hamiltonian to include thermal effects<latexit sha1_base64="0ejNNxGUm5M/hQiiar2O4grDRIQ=">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</latexit>

Ground state occupancy

PN =

N
X
fn

n=1

2

(a)
(a)

0.6
0.6

PinnedPinned

0.4
0.4
0.2
0.2

(b)
(b)

fi

￼

0.6
0.6

0.5
0.5

0.8
0.8

1
1

1

0.5
5

2.5

0

2.5

5

0

PinnedPinned

0

0.1

0.2
0.3
T /Tf (gm = 3)

0.4

Thermal

0.6
0.4
0.2
(b)

0.1

0.5
0.5
0

0.4
0.4

0

0.2
0.3
0.2
0.3
T /Tf (gm = 3)
T /Tf (gm = 3)

0.2

5
50
0

PinnedPinned
0.1
0.1

0.4

2.5
2.5

Pinned0.2

ThermalThermal

T /Tf

0
0

0

PinnedPinned

0.8

0.5

1

0.4
0.4

T /Tf
T /Tf

0.6

q
⇤ )2 ✏
1
+
2
(f
1
Tcrit
p
= C(f ⇤ )Tf
1 + 2✏ 1

gmgm

2.5
2.5

0.2
0.2

0.4
0.4

0.4

5
5

0
0

Tcrit
<latexit sha1_base64="C/PDjGsn5AqLzGHM3lk+60pxxvc=">AAAB9HicbVBNS8NAEJ3Ur1q/qh69BIvgqSQi6rHoxWOFfkEbyma7aZduNnF3Uiyhv8OLB0W8+mO8+W/ctDlo64OBx3szzMzzY8E1Os63VVhb39jcKm6Xdnb39g/Kh0ctHSWKsiaNRKQ6PtFMcMmayFGwTqwYCX3B2v74LvPbE6Y0j2QDpzHzQjKUPOCUoJG8Rr+H7AlTqjjO+uWKU3XmsFeJm5MK5Kj3y1+9QUSTkEmkgmjddZ0YvZQo5FSwWamXaBYTOiZD1jVUkpBpL50fPbPPjDKwg0iZkmjP1d8TKQm1noa+6QwJjvSyl4n/ed0Egxsv5TJOkEm6WBQkwsbIzhKwB1wximJqCMn+5tSmI6IIRZNTyYTgLr+8SloXVfeq6j5cVmq3eRxFOIFTOAcXrqEG91CHJlB4hGd4hTdrYr1Y79bHorVg5TPH8AfW5w9ge5KA</latexit>

0.3
0.3

(a)

1
fpin =
exp [ (E(fpin ) µ(fpin ))] + 1<latexit sha1_base64="smuoYS8+hVYrGtyySbHD6ImCXD4=">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</latexit>

0.2
0.2

Thermalneeds a self-consistency criterion for finding the energies and occupations<latexit sha1_base64="LFXpKD0NErkPQ++sBmyvRRItW5o=">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</latexit>

0.1
0.1

0.3

0
00
0

0.8

reduced interaction changes the energy E′1 and therefore f1, etc…

one can estimate a critical temperature for the pinned state phasetransition from the point where the change in the ground state occupancy
is maximal

ThermalThermal1

temperature effectively reduces the interaction!

0.8
0.8

PN
PN

gc

| 1 (x)|

1
1PN

Ĥe↵ =

1 @
2 @x2

2
gm
f1

gm

2

<latexit sha1_base64="P3pL4iajY00pAUhIeAkVs25TmSI=">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</latexit>

N

ff

ff

But there is more. Quantum can also do stu di erently…

Quantum Tech: Work & Heat & Engines
two fundamental forms of energy transfer

macroscopic

microscopic<latexit sha1_base64="3h8kZ2VxPzW08/s8k8rS4AoM0PI=">AAAB/3icbVDLSsNAFJ3UV62vqODGzWARXJVEiroRig9wJRXsA5oQJtNJO3RmEmYmQold+CtuXCji1t9w5984bbPQ1gMXDufcy733hAmjSjvOt1VYWFxaXimultbWNza37O2dpopTiUkDxyyW7RApwqggDU01I+1EEsRDRlrh4HLstx6IVDQW93qYEJ+jnqARxUgbKbD3WueeSnkgYBQI74owjeB1cBvYZafiTADniZuTMshRD+wvrxvjlBOhMUNKdVwn0X6GpKaYkVHJSxVJEB6gHukYKhAnys8m94/goVG6MIqlKaHhRP09kSGu1JCHppMj3Vez3lj8z+ukOjrzMyqSVBOBp4uilEEdw3EYsEslwZoNDUFYUnMrxH0kEdYmspIJwZ19eZ40jyvuSaV6Vy3XLvI4imAfHIAj4IJTUAM3oA4aAINH8AxewZv1ZL1Y79bHtLVg5TO74A+szx/C/pVN</latexit>Work:energy change induced by the variation of a mechanical parameter

displacement of energy levels in quantum systems

W =X

f n ENnHeat:<latexit sha1_base64="kaSdt1z3FaDmkQiRIiz1ubI3aas=">AAACAHicbZDLSgMxFIYz9VbrbdSFCzfBIrgqM1LUjVC8gCtpwV6gMwyZNNOGJpkhyQhl6MZXceNCEbc+hjvfxrSdhbb+EPj4zzmcnD9MGFXacb6twtLyyupacb20sbm1vWPv7rVUnEpMmjhmseyESBFGBWlqqhnpJJIgHjLSDofXk3r7kUhFY/GgRwnxOeoLGlGMtLEC+6Bx6amUBwJ6N4RpBCODt8F9YJedijMVXAQ3hzLIVQ/sL68X45QToTFDSnVdJ9F+hqSmmJFxyUsVSRAeoj7pGhSIE+Vn0wPG8Ng4PRjF0jyh4dT9PZEhrtSIh6aTIz1Q87WJ+V+tm+rows+oSFJNBJ4tilIGdQwnacAelQRrNjKAsKTmrxAPkERYm8xKJgR3/uRFaJ1W3LNKtVEt167yOIrgEByBE+CCc1ADd6AOmgCDMXgGr+DNerJerHfrY9ZasPKZffBH1ucPFRaVcQ==</latexit>

energy exchanged with a thermal bathmodi cation of a systems population probability distribution

Q=

X
n

Heat Engine:

convert thermal energy into mechanical work by cyclically operating between e ective thermal reservoirs at di erent temperatures
heating/cooling strokes redistribute the quantum state populations

Quantum Heat Engine: uses quantum e ects in the heat engine process (squeezed baths, quantum STAs, etc)

ff

uses genuinely non-classical forms of energies in a heat-engine-like cycle
ff

ff

fi

Quantum Engine:f n EN

Otto Cycle
consider a gas of particles in a harmonic traphW3 i<latexit sha1_base64="T2jOGVncTndCzfH+7yU5QjEV6LM=">AAAB+3icbZDLSsNAFIYn9VbrLdalm8EiuCqJFu2y4MZlBXuBJoTJ9KQdOpmEmYlYSl/FjQtF3Poi7nwbp2kW2vrDwMd/zuGc+cOUM6Ud59sqbWxube+Udyt7+weHR/ZxtauSTFLo0IQnsh8SBZwJ6GimOfRTCSQOOfTCye2i3nsEqVgiHvQ0BT8mI8EiRok2VmBXPU7EiAPuBVeezDGwa07dyYXXwS2ghgq1A/vLGyY0i0FoyolSA9dJtT8jUjPKYV7xMgUpoRMygoFBQWJQ/iy/fY7PjTPEUSLNExrn7u+JGYmVmsah6YyJHqvV2sL8rzbIdNT0Z0ykmQZBl4uijGOd4EUQeMgkUM2nBgiVzNyK6ZhIQrWJq2JCcFe/vA7dy7p7XW/cN2qtZhFHGZ2iM3SBXHSDWugOtVEHUfSEntErerPm1ov1bn0sW0tWMXOC/sj6/AFzyZQL</latexit>✏2<latexit sha1_base64="pc7NjokFIHH5Ga02FNe+mt7Loyw=">AAAB8XicbVBNS8NAEJ3Ur1q/qh69BIvgqSSlaI8FLx4r2FZsQ9lsJ+3SzW7Y3Qgl9F948aCIV/+NN/+N2zYHbX0w8Hhvhpl5YcKZNp737RQ2Nre2d4q7pb39g8Oj8vFJR8tUUWxTyaV6CIlGzgS2DTMcHxKFJA45dsPJzdzvPqHSTIp7M00wiMlIsIhRYqz02MdEMy7FoDYoV7yqt4C7TvycVCBHa1D+6g8lTWMUhnKidc/3EhNkRBlGOc5K/VRjQuiEjLBnqSAx6iBbXDxzL6wydCOpbAnjLtTfExmJtZ7Goe2MiRnrVW8u/uf1UhM1goyJJDUo6HJRlHLXSHf+vjtkCqnhU0sIVcze6tIxUYQaG1LJhuCvvrxOOrWqf1Wt39UrzUYeRxHO4BwuwYdraMIttKANFAQ8wyu8Odp5cd6dj2VrwclnTuEPnM8feYGQxA==</latexit>

heat stroke changes temperatureenergychanges the distribution function
hQ4 i<latexit sha1_base64="il0NRJa4iEEyIeJwAq4WilAyXa0=">AAAB+3icbZDLSsNAFIYn9VbrLdalm8EiuCqJFO2y4MZlC/YCTQiT6Wk7dDIJMxOxhL6KGxeKuPVF3Pk2TtMstPWHgY//nMM584cJZ0o7zrdV2tre2d0r71cODo+OT+zTak/FqaTQpTGP5SAkCjgT0NVMcxgkEkgUcuiHs7tlvf8IUrFYPOh5An5EJoKNGSXaWIFd9TgREw64EzQ8mWNg15y6kwtvgltADRVqB/aXN4ppGoHQlBOlhq6TaD8jUjPKYVHxUgUJoTMygaFBQSJQfpbfvsCXxhnhcSzNExrn7u+JjERKzaPQdEZET9V6bWn+Vxumetz0MyaSVIOgq0XjlGMd42UQeMQkUM3nBgiVzNyK6ZRIQrWJq2JCcNe/vAm967p7U290GrVWs4ijjM7RBbpCLrpFLXSP2qiLKHpCz+gVvVkL68V6tz5WrSWrmDlDf2R9/gBsBpQG</latexit><latexit sha1_base64="GT8MqT+PiOLN1prQ+RVEBegUHoA=">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</latexit>

hQ2 i<latexit sha1_base64="BGYZnPNjGT2J2gBDAQNmfpIBvdA=">AAAB+3icbZDNSsNAFIVv6l+tf7Eu3QwWwVVJStEuC25ctmBboQlhMp20QyeTMDMRS+iruHGhiFtfxJ1v4zTtQlsPDHycey/3zglTzpR2nG+rtLW9s7tX3q8cHB4dn9in1b5KMklojyQ8kQ8hVpQzQXuaaU4fUklxHHI6CKe3i/rgkUrFEnGvZyn1YzwWLGIEa2MFdtXjWIw5Rd2g4ckCA7vm1J1CaBPcFdRgpU5gf3mjhGQxFZpwrNTQdVLt51hqRjidV7xM0RSTKR7ToUGBY6r8vLh9ji6NM0JRIs0TGhXu74kcx0rN4tB0xlhP1HptYf5XG2Y6avk5E2mmqSDLRVHGkU7QIgg0YpISzWcGMJHM3IrIBEtMtImrYkJw17+8Cf1G3b2uN7vNWru1iqMM53ABV+DCDbThDjrQAwJP8Ayv8GbNrRfr3fpYtpas1cwZ/JH1+QNo8JQE</latexit>✏1<latexit sha1_base64="415rxb1RFmTY6Jtx6WwVNkvANfk=">AAAB73icbVDLSgNBEOyNrxhfUY9eBoPgKexK0BwDXjxGMA9IljA7mU2GzGOdmRXCkp/w4kERr/6ON//GSbIHTSxoKKq66e6KEs6M9f1vr7CxubW9U9wt7e0fHB6Vj0/aRqWa0BZRXOluhA3lTNKWZZbTbqIpFhGnnWhyO/c7T1QbpuSDnSY0FHgkWcwItk7q9pWgIzwIBuWKX/UXQOskyEkFcjQH5a/+UJFUUGkJx8b0Aj+xYYa1ZYTTWamfGppgMsEj2nNUYkFNmC3unaELpwxRrLQradFC/T2RYWHMVESuU2A7NqveXPzP66U2rocZk0lqqSTLRXHKkVVo/jwaMk2J5VNHMNHM3YrIGGtMrIuo5EIIVl9eJ+2ranBdrd3XKo16HkcRzuAcLiGAG2jAHTShBQQ4PMMrvHmP3ov37n0sWwtePnMKf+B9/gC5c4++</latexit>!1<latexit sha1_base64="u8RIqK+Lv/a94SHMU5GUgvGamXo=">AAAB73icbVDLSgNBEJz1GeMr6tHLYBA8hd0QNMeAF48RzAOSJcxOepMh81hnZoWw5Ce8eFDEq7/jzb9xkuxBEwsaiqpuuruihDNjff/b29jc2t7ZLewV9w8Oj45LJ6dto1JNoUUVV7obEQOcSWhZZjl0Ew1ERBw60eR27neeQBum5IOdJhAKMpIsZpRYJ3X7SsCIDKqDUtmv+AvgdRLkpIxyNAelr/5Q0VSAtJQTY3qBn9gwI9oyymFW7KcGEkInZAQ9RyURYMJsce8MXzpliGOlXUmLF+rviYwIY6Yicp2C2LFZ9ebif14vtXE9zJhMUguSLhfFKcdW4fnzeMg0UMunjhCqmbsV0zHRhFoXUdGFEKy+vE7a1UpwXand18qNeh5HAZ2jC3SFAnSDGugONVELUcTRM3pFb96j9+K9ex/L1g0vnzlDf+B9/gC694+/</latexit>

trap frequency

exp

⇣

En µ
kB T

⌘

±1

energy is added to the engine

hW1 i<latexit sha1_base64="WiiGosEqPJvRVUjeYJNSGHxq5mI=">AAAB+3icbZDLSsNAFIZP6q3WW6xLN4NFcFUSEe2y4MZlBXuBJoTJdNIOnUzCzEQsoa/ixoUibn0Rd76N0zQLbf1h4OM/53DO/GHKmdKO821VNja3tnequ7W9/YPDI/u43lNJJgntkoQnchBiRTkTtKuZ5nSQSorjkNN+OL1d1PuPVCqWiAc9S6kf47FgESNYGyuw6x7HYswp6geuJwsM7IbTdAqhdXBLaECpTmB/eaOEZDEVmnCs1NB1Uu3nWGpGOJ3XvEzRFJMpHtOhQYFjqvy8uH2Ozo0zQlEizRMaFe7viRzHSs3i0HTGWE/Uam1h/lcbZjpq+TkTaaapIMtFUcaRTtAiCDRikhLNZwYwkczcisgES0y0iatmQnBXv7wOvcume928ur9qtFtlHFU4hTO4ABduoA130IEuEHiCZ3iFN2tuvVjv1seytWKVMyfwR9bnD3CzlAk=</latexit><latexit sha1_base64="MYUHkZxsnS+oUGu024hrEatT7VY=">AAAB8XicbVBNS8NAEJ3Ur1q/qh69LBbBU0mkaI8FLx4r2A9sQ9lsJ+3SzSbsboQS+i+8eFDEq//Gm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ7dzvPKHSPJYPZpqgH9GR5CFn1FjpsY+J5iKWA29QrrhVdwGyTrycVCBHc1D+6g9jlkYoDRNU657nJsbPqDKcCZyV+qnGhLIJHWHPUkkj1H62uHhGLqwyJGGsbElDFurviYxGWk+jwHZG1Iz1qjcX//N6qQnrfsZlkhqUbLkoTAUxMZm/T4ZcITNiagllittbCRtTRZmxIZVsCN7qy+ukfVX1rqu1+1qlUc/jKMIZnMMleHADDbiDJrSAgYRneIU3RzsvzrvzsWwtOPnMKfyB8/kDd/2Qww==</latexit>

fn =

1

!2

but there are other ways one can change the distribution function: change the chemical potential
or change the quantum part by turning the ‘plus one’ into a ‘minus one’ or v.v.

<latexit sha1_base64="RAcBJWYzHJA9X+y1UWgFkFXalfI=">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</latexit>

fn =

exp

⇣

1
En µ
kB T

⌘

switch the working medium cyclically from a Bose-Einstein statistics to a Fermi-Dirac statistics±1

at xed temperature

T =0<latexit sha1_base64="/VfoJsl2c7iaoPEAsyACvOwYym0=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKexK0FyEgBePEfOCZAmzk0kyZHZ2mekVwpJP8OJBEa9+kTf/xkmyB00saCiquunuCmIpDLrut5Pb2Nza3snvFvb2Dw6PiscnLRMlmvEmi2SkOwE1XArFmyhQ8k6sOQ0DydvB5G7ut5+4NiJSDZzG3A/pSImhYBSt9Ni4dfvFklt2FyDrxMtICTLU+8Wv3iBiScgVMkmN6XpujH5KNQom+azQSwyPKZvQEe9aqmjIjZ8uTp2RC6sMyDDSthSShfp7IqWhMdMwsJ0hxbFZ9ebif143wWHVT4WKE+SKLRcNE0kwIvO/yUBozlBOLaFMC3srYWOqKUObTsGG4K2+vE5aV2Xvulx5qJRq1SyOPJzBOVyCBzdQg3uoQxMYjOAZXuHNkc6L8+58LFtzTjZzCn/gfP4An4eNWA==</latexit>

bosonsfermions
Remember:<latexit sha1_base64="S3EoPxNcERX4SK+PLHH96JY8Mzg=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKexK0BwDoniMaB6QLGF2MpsMmZ1dZnqFEPIJXjwo4tUv8ubfOEn2oIkFDUVVN91dQSKFQdf9dnJr6xubW/ntws7u3v5B8fCoaeJUM95gsYx1O6CGS6F4AwVK3k40p1EgeSsYXc/81hPXRsTqEccJ9yM6UCIUjKKVHm56t71iyS27c5BV4mWkBBnqveJXtx+zNOIKmaTGdDw3QX9CNQom+bTQTQ1PKBvRAe9YqmjEjT+ZnzolZ1bpkzDWthSSufp7YkIjY8ZRYDsjikOz7M3E/7xOimHVnwiVpMgVWywKU0kwJrO/SV9ozlCOLaFMC3srYUOqKUObTsGG4C2/vEqaF2Xvsly5r5Rq1SyOPJzAKZyDB1dQgzuoQwMYDOAZXuHNkc6L8+58LFpzTjZzDH/gfP4A3a+NgQ==</latexit>

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Q=

X
n

Bose-Einstein condensate

Fermi sea

rst idea: use nuclear processes! Hard to do cyclically, known nuclear decay processes do not change statistics,….
use BEC-BCS transition region, where fermionic atoms can be turned into bosonic molecules via a Feshbach resonancefi

fi

Statistical Quantum Engine Considerations

f n ENPauli Engine

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0

fermionisation

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1C

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bosonisation

Interaction parameter 1/kf acyclically converts energy stemming from the Pauli exclusion principle (”Pauli energy”) into mechanical work

E2P
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W1<latexit sha1_base64="2Wv5ptmGIvppLR8c8p5Q3ojSPwM=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mkqMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz00O57/XLFrbpzkFXi5aQCORr98ldvELM0QmmYoFp3PTcxfkaV4UzgtNRLNSaUjekQu5ZKGqH2s/mpU3JmlQEJY2VLGjJXf09kNNJ6EgW2M6JmpJe9mfif101NeO1nXCapQckWi8JUEBOT2d9kwBUyIyaWUKa4vZWwEVWUGZtOyYbgLb+8SloXVe+yWruvVeo3eRxFOIFTOAcPrqAOd9CAJjAYwjO8wpsjnBfn3flYtBacfOYY/sD5/AHcSY2I</latexit>>1

compression

A

B<latexit sha1_base64="415rxb1RFmTY6Jtx6WwVNkvANfk=">AAAB73icbVDLSgNBEOyNrxhfUY9eBoPgKexK0BwDXjxGMA9IljA7mU2GzGOdmRXCkp/w4kERr/6ON//GSbIHTSxoKKq66e6KEs6M9f1vr7CxubW9U9wt7e0fHB6Vj0/aRqWa0BZRXOluhA3lTNKWZZbTbqIpFhGnnWhyO/c7T1QbpuSDnSY0FHgkWcwItk7q9pWgIzwIBuWKX/UXQOskyEkFcjQH5a/+UJFUUGkJx8b0Aj+xYYa1ZYTTWamfGppgMsEj2nNUYkFNmC3unaELpwxRrLQradFC/T2RYWHMVESuU2A7NqveXPzP66U2rocZk0lqqSTLRXHKkVVo/jwaMk2J5VNHMNHM3YrIGGtMrIuo5EIIVl9eJ+2ranBdrd3XKo16HkcRzuAcLiGAG2jAHTShBQQ4PMMrvHmP3ov37n0sWwtePnMKf+B9/gC5c4++</latexit><latexit sha1_base64="XN4W29tM/mx4gkmxgSA4uZp9+b0=">AAAB+nicbVDLSgMxFM3UV62vqS7dBIvgqsyIqMuqG5cV7AM6w5BJM21oHkOSUUrtp7hxoYhbv8Sdf2OmnYW2HggczrmHe3PilFFtPO/bKa2srq1vlDcrW9s7u3tudb+tZaYwaWHJpOrGSBNGBWkZahjppoogHjPSiUc3ud95IEpTKe7NOCUhRwNBE4qRsVLkVgNp7TwdSE4GKLqK3JpX92aAy8QvSA0UaEbuV9CXOONEGMyQ1j3fS004QcpQzMi0EmSapAiP0ID0LBWIEx1OZqdP4bFV+jCRyj5h4Ez9nZggrvWYx3aSIzPUi14u/uf1MpNchhMq0swQgeeLkoxBI2HeA+xTRbBhY0sQVtTeCvEQKYSNbatiS/AXv7xM2qd1/7x+dndWa1wXdZTBITgCJ8AHF6ABbkETtAAGj+AZvII358l5cd6dj/loySkyB+APnM8fddyUIw==</latexit>

advantages:!A<latexit sha1_base64="ZwSAdxzY/8PMDzAbk6c7l2v/eNs=">AAAB+nicbVDLSgMxFM3UV62vqS7dBIvgqsyIqMtSNy4r2Ad0hiGTZtrQPIYko5TaT3HjQhG3fok7/8ZMOwttPRA4nHMP9+bEKaPaeN63U1pb39jcKm9Xdnb39g/c6mFHy0xh0saSSdWLkSaMCtI21DDSSxVBPGakG49vcr/7QJSmUtybSUpCjoaCJhQjY6XIrQbS2nk6kJwMUdSM3JpX9+aAq8QvSA0UaEXuVzCQOONEGMyQ1n3fS004RcpQzMisEmSapAiP0ZD0LRWIEx1O56fP4KlVBjCRyj5h4Fz9nZgirvWEx3aSIzPSy14u/uf1M5Nch1Mq0swQgReLkoxBI2HeAxxQRbBhE0sQVtTeCvEIKYSNbatiS/CXv7xKOud1/7J+cXdRazSLOsrgGJyAM+CDK9AAt6AF2gCDR/AMXsGb8+S8OO/Ox2K05BSZI/AHzucPd2CUJA==</latexit>

trap frequency

fully reversible process
no coupling to a bath required
minimal dissipation, entropy constant!B!1<latexit sha1_base64="u8RIqK+Lv/a94SHMU5GUgvGamXo=">AAAB73icbVDLSgNBEJz1GeMr6tHLYBA8hd0QNMeAF48RzAOSJcxOepMh81hnZoWw5Ce8eFDEq7/jzb9xkuxBEwsaiqpuuruihDNjff/b29jc2t7ZLewV9w8Oj45LJ6dto1JNoUUVV7obEQOcSWhZZjl0Ew1ERBw60eR27neeQBum5IOdJhAKMpIsZpRYJ3X7SsCIDKqDUtmv+AvgdRLkpIxyNAelr/5Q0VSAtJQTY3qBn9gwI9oyymFW7KcGEkInZAQ9RyURYMJsce8MXzpliGOlXUmLF+rviYwIY6Yicp2C2LFZ9ebif14vtXE9zJhMUguSLhfFKcdW4fnzeMg0UMunjhCqmbsV0zHRhFoXUdGFEKy+vE7a1UpwXand18qNeh5HAZ2jC3SFAnSDGugONVELUcTRM3pFb96j9+K9ex/L1g0vnzlDf+B9/gC694+/</latexit>

trap frequency!2Performance of the Pauli Engine

BFB = BC = BD = 832.2G

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W
⌘= P
E2
<latexit sha1_base64="S0HRJ+YHkZdbyV/f3zazd4ZMBSY=">AAAB/XicbVDLSsNAFL2pr1pf8bFzEyyCq5KUom6EogguK9gHNLFMppN26GQSZiZCDcFfceNCEbf+hzv/xmmbhbYeuHA4517uvcePGZXKtr+NwtLyyupacb20sbm1vWPu7rVklAhMmjhikej4SBJGOWkqqhjpxIKg0Gek7Y+uJn77gQhJI36nxjHxQjTgNKAYKS31zAOXKHThBgLhtJ2l173qfSPrmWW7Yk9hLRInJ2XI0eiZX24/wklIuMIMSdl17Fh5KRKKYkaykptIEiM8QgPS1ZSjkEgvnV6fWcda6VtBJHRxZU3V3xMpCqUch77uDJEaynlvIv7ndRMVnHsp5XGiCMezRUHCLBVZkyisPhUEKzbWBGFB9a0WHiKdhNKBlXQIzvzLi6RVrTinldptrVy/zOMowiEcwQk4cAZ1uIEGNAHDIzzDK7wZT8aL8W58zFoLRj6zD39gfP4AMr2VEg==</latexit>

work strokes

statistics strokes<latexit sha1_base64="+68s8oh1jL299dduCsKhWttdP2w=">AAAB83icbVBNS8NAEJ3Ur1q/qh69LBahIpZEi3oRil48VrBNoQ1hs920SzebsLsRSujf8OJBEa/+GW/+G7dtDlp9MPB4b4aZeUHCmdK2/WUVlpZXVteK66WNza3tnfLuXlvFqSS0RWIey06AFeVM0JZmmtNOIimOAk7dYHQ79d1HKhWLxYMeJ9SL8ECwkBGsjdRzr0+rru+cuP75sV+u2DV7BvSXODmpQI6mX/7s9WOSRlRowrFSXcdOtJdhqRnhdFLqpYommIzwgHYNFTiiystmN0/QkVH6KIylKaHRTP05keFIqXEUmM4I66Fa9Kbif1431eGVlzGRpJoKMl8UphzpGE0DQH0mKdF8bAgmkplbERliiYk2MZVMCM7iy39J+6zmXNTq9/VK4yaPowgHcAhVcOASGnAHTWgBgQSe4AVerdR6tt6s93lrwcpn9uEXrI9verWQCA==</latexit>(W1 + W3 )e ciency<latexit sha1_base64="5HcNuMQMViYI9P6vW9qRLeqfzig=">AAACBXicbVA7T8MwGHR4lvIKMMIQUSGVpUpQVRgLLIxFog+pCZHjOq1VPyLbQaqiLiz8FRYGEGLlP7Dxb3DbDNBykqXT3X22v4sSSpR23W9raXlldW29sFHc3Nre2bX39ltKpBLhJhJUyE4EFaaE46YmmuJOIjFkEcXtaHg98dsPWCoi+J0eJThgsM9JTBDURgrto7Ln3tf8QQSlL0xwco8vGO7D8PI0tEtuxZ3CWSReTkogRyO0v/yeQCnDXCMKlep6bqKDDEpNEMXjop8qnEA0hH3cNZRDhlWQTbcYOydG6TmxkOZw7UzV3xMZZEqNWGSSDOqBmvcm4n9eN9XxRZARnqQaczR7KE6po4UzqcTpEYmRpiNDIJLE/NVBAygh0qa4oinBm195kbTOKl6tUr2tlupXeR0FcAiOQRl44BzUwQ1ogCZA4BE8g1fwZj1ZL9a79TGLLln5zAH4A+vzB0RQl9A=</latexit><latexit sha1_base64="5HcNuMQMViYI9P6vW9qRLeqfzig=">AAACBXicbVA7T8MwGHR4lvIKMMIQUSGVpUpQVRgLLIxFog+pCZHjOq1VPyLbQaqiLiz8FRYGEGLlP7Dxb3DbDNBykqXT3X22v4sSSpR23W9raXlldW29sFHc3Nre2bX39ltKpBLhJhJUyE4EFaaE46YmmuJOIjFkEcXtaHg98dsPWCoi+J0eJThgsM9JTBDURgrto7Ln3tf8QQSlL0xwco8vGO7D8PI0tEtuxZ3CWSReTkogRyO0v/yeQCnDXCMKlep6bqKDDEpNEMXjop8qnEA0hH3cNZRDhlWQTbcYOydG6TmxkOZw7UzV3xMZZEqNWGSSDOqBmvcm4n9eN9XxRZARnqQaczR7KE6po4UzqcTpEYmRpiNDIJLE/NVBAygh0qa4oinBm195kbTOKl6tUr2tlupXeR0FcAiOQRl44BzUwQ1ogCZA4BE8g1fwZj1ZL9a79TGLLln5zAH4A+vzB0RQl9A=</latexit>

energy change (106 ~! A )Work output (106 ~! A )W =compression ratio ! B /! A<latexit sha1_base64="ciFJkLzcs8V0OXvaH6JoQQErORs=">AAACDHicbVDLSgMxFM3UV62vqks3wSK4qjNS1GWtG5cV7AM6Q8mkmTY0jyHJCGXoB7jxV9y4UMStH+DOvzHTzkJbDwQO55zLzT1hzKg2rvvtFFZW19Y3ipulre2d3b3y/kFby0Rh0sKSSdUNkSaMCtIy1DDSjRVBPGSkE45vMr/zQJSmUtybSUwCjoaCRhQjY6V+ueJLa2fTvuRkiPqNs0Xl2qbcqjsDXCZeTiogR7Nf/vIHEiecCIMZ0rrnubEJUqQMxYxMS36iSYzwGA1Jz1KBONFBOjtmCk+sMoCRVPYJA2fq74kUca0nPLRJjsxIL3qZ+J/XS0x0FaRUxIkhAs8XRQmDRsKsGTigimDDJpYgrKj9K8QjpBA2tr+SLcFbPHmZtM+r3kW1dler1Bt5HUVwBI7BKfDAJaiDW9AELYDBI3gGr+DNeXJenHfnYx4tOPnMIfgD5/MHVNCbzA==</latexit>

compression ratio ! B /! A

compression ratio ! B /! A<latexit sha1_base64="ciFJkLzcs8V0OXvaH6JoQQErORs=">AAACDHicbVDLSgMxFM3UV62vqks3wSK4qjNS1GWtG5cV7AM6Q8mkmTY0jyHJCGXoB7jxV9y4UMStH+DOvzHTzkJbDwQO55zLzT1hzKg2rvvtFFZW19Y3ipulre2d3b3y/kFby0Rh0sKSSdUNkSaMCtIy1DDSjRVBPGSkE45vMr/zQJSmUtybSUwCjoaCRhQjY6V+ueJLa2fTvuRkiPqNs0Xl2qbcqjsDXCZeTiogR7Nf/vIHEiecCIMZ0rrnubEJUqQMxYxMS36iSYzwGA1Jz1KBONFBOjtmCk+sMoCRVPYJA2fq74kUca0nPLRJjsxIL3qZ+J/XS0x0FaRUxIkhAs8XRQmDRsKsGTigimDDJpYgrKj9K8QjpBA2tr+SLcFbPHmZtM+r3kW1dler1Bt5HUVwBI7BKfDAJaiDW9AELYDBI3gGr+DNeXJenHfnYx4tOPnMIfgD5/MHVNCbzA==</latexit><latexit sha1_base64="ciFJkLzcs8V0OXvaH6JoQQErORs=">AAACDHicbVDLSgMxFM3UV62vqks3wSK4qjNS1GWtG5cV7AM6Q8mkmTY0jyHJCGXoB7jxV9y4UMStH+DOvzHTzkJbDwQO55zLzT1hzKg2rvvtFFZW19Y3ipulre2d3b3y/kFby0Rh0sKSSdUNkSaMCtIy1DDSjRVBPGSkE45vMr/zQJSmUtybSUwCjoaCRhQjY6V+ueJLa2fTvuRkiPqNs0Xl2qbcqjsDXCZeTiogR7Nf/vIHEiecCIMZ0rrnubEJUqQMxYxMS36iSYzwGA1Jz1KBONFBOjtmCk+sMoCRVPYJA2fq74kUca0nPLRJjsxIL3qZ+J/XS0x0FaRUxIkhAs8XRQmDRsKsGTigimDDJpYgrKj9K8QjpBA2tr+SLcFbPHmZtM+r3kW1dler1Bt5HUVwBI7BKfDAJaiDW9AELYDBI3gGr+DNeXJenHfnYx4tOPnMIfgD5/MHVNCbzA==</latexit>

work output and e ciency increase with (experimentally accessible)
compressions ratios
e ciencies are signi cant (>10%) for modest aspect ratios already

ffi

fi

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J. Koch, K. Menon, E. Cuestas, S. Barbosa, E. Lutz, T. Fogarty, TB, A. Widera, arXiv:2209.14202 (2022)

for compression ratios larger than 10, theoretically e ciencies > 50% possible

Summary and outlook
ultracold atoms are highly suitable systems to build
quantum simulators, which can have applications
in many di erent areas

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gm = 10| (x)|20<latexit sha1_base64="S3EoPxNcERX4SK+PLHH96JY8Mzg=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKexK0BwDoniMaB6QLGF2MpsMmZ1dZnqFEPIJXjwo4tUv8ubfOEn2oIkFDUVVN91dQSKFQdf9dnJr6xubW/ntws7u3v5B8fCoaeJUM95gsYx1O6CGS6F4AwVK3k40p1EgeSsYXc/81hPXRsTqEccJ9yM6UCIUjKKVHm56t71iyS27c5BV4mWkBBnqveJXtx+zNOIKmaTGdDw3QX9CNQom+bTQTQ1PKBvRAe9YqmjEjT+ZnzolZ1bpkzDWthSSufp7YkIjY8ZRYDsjikOz7M3E/7xOimHVnwiVpMgVWywKU0kwJrO/SV9ozlCOLaFMC3srYUOqKUObTsGG4C2/vEqaF2Xvsly5r5Rq1SyOPJzAKZyDB1dQgzuoQwMYDOAZXuHNkc6L8+58LFpzTjZzDH/gfP4A3a+NgQ==</latexit>

EF

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Tim Keller, T. Fogarty, TB, Phys. Rev. Lett. 128, 053401 (2022)
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(a)

gm = 1µ0 /gcgm = 0Das Team
Pham Le Kien
Thomás Fogarty
Karol Gietka
Eloisa Cuestas
Hao Lyu
Seyyare Aksu
Kritika Jain
Christopher Campbell
Tim Keller
Friederike Metz
Lewis Ruks
Muhammad Sirajul
Mohamed Boubakour
Jose Carlos Pelayo
Keerthy Menon

Jennifer Koch (KL)Sian Babosa (KL)

Artur Widera (KL)

Eric Lutz (Stuttgart)

Tai Tran
Hoshu Hiyane
Sarika Sasidharan Nair
Sawako Koki