Mikhail Lemeshko

Quantum Fluid Clusters May 20, 2019

Institute of Science and Technology (IST) Austria

Quasiparticle approach to far-from-equilibrium dynamics

of molecules in helium nanodroplets

Electrons in solids Molecules in solvents

Ultrafast magnetism, Data storage, Spintronics, Quantum computation, …

Controlling chemical reactions, Catalysis, Energy research, …

yyyy LS

J

J = |L–S| ... |L+S|

Condensed-matter systems: is it possible at all?

The problem

Quantum angular momentum

Small systems: extremely challenging

(electrons in an atom)

Initial motivation: molecules in superfluid helium nanodroplets

Angew. Chem. Int. Ed. 43, 2622 (2004) Andrew M. Ellis webpage

Reasons people do it: • Spectroscopy (0.4 K, no doppler shift)• Studying unstable species (radicals)

Free

in He

in He3

4

“Clean” rotational spectra,

but renormalized rotational constant

01

2

3J =

There are qualitative explanations (two-fluid model, etc.),Quantum Monte Carlo calculations for several molecules (Zillich, Whaley, …)

However, no general microscopic understanding

Initial motivation: molecules in superfluid helium nanodroplets

Dynamics of molecules in droplets:even qualitative understanding was absent

Revivals of rotational wavepackets Bloch sphere analogy

Create

MeasureStapelfeldt group, PRL 110, 093002 (2013)

Initial motivation: molecules in superfluid helium nanodroplets

Molecule in He droplet as a quantum impurity problem

Electrons in solidsMolecules in solution

Molecular M

odelling

Basics (2010)

Atoms in BEC

Impurity problems: 1 particle + its many-body environment

Still ~10 degrees of freedom – challenging to understand23

A physicist’s trick: introducing “quasiparticles”

Strongly interacting system of real particles

Almost free motion of imaginary quasiparticles

R. Mattuck, “A Guide to Feynman Diagrams in the Many-body Problem”

Quasiparticles: examples

Hole:an empty spot in a sea of electrons

http://w

ww

.allaboutcircuits.com

Nature 485, 588–589

Polaron:an impurity whose linear motion

is “dressed” by a cloud of excitations

Can molecules in superfluids be described as quasiparticles?

Free

in He4

Molecules in He:

effective rotational constant

Angew. Chem. Int. Ed. 43, 2622 (2004)

Electrons in solids: effective mass

Polaron quasiparticle ‘Angulon’ quasiparticle?

Why do we need another one?

It’d describe (in principle) any many-body system with angular momentum

Rydberg atoms / cold molecules in a BEC / Fermi gas

Pfau group, Nature 502, 664 (2013)

Hybrid organic/inorganic perovskites

Electrons in solids

Angew. Chem. Int. Ed. 43, 2622 (2004)

Chemistry in solvents

(Einstein-de Haas effect)

Bakulin et al., J. Phys. Chem. Lett. 6, 3663 (2015)

The angulon Hamiltonian

molecule phonons molecule-phonon interactions

z ( ,̂ ˆ)z

x

y

( , )z

yy

( ,(

x

y

zz

y

x • Was derived exactly for a molecule

in a weakly-interacting superfluid (BEC)

• Can be used as a phenomenological model for any bosonic bath

R. Schmidt and ML, Phys. Rev. Lett. 114, 203001 (2015) R. Schmidt and ML, Phys. Rev. X 6, 011012 (2016)

ML, Phys. Rev. Lett. 118, 095301 (2017)

The angulon Hamiltonian

molecule phonons molecule-phonon interactions

z ( ,̂ ˆ)z

x

y

( , )z

yy

( ,(

x

y

zz

y

x

angulonquantum

rotormany-body field

The “angulon” quasiparticle

ML, Phys. Rev. Lett. 118, 095301 (2017)

Existence of angulons

Viewpoint: Yu. Shchadilova, Physics 10, 20 (2017)

B*/B

Experiment:

OH

HF

LiH

CH4 NH3

HCl

H2O

CONO

HCNDCN

H2C2

N2O

I2

CO2

OCS

CS2

SF6

CH3

HCCCN

0.01 0.02 0.03 0.04 0.05 0.060.0

0.2

0.4

0.6

0.8

1.0

γ

0.3 0.4 0.5 0.6 0.7 0.8 0.90.0

0.2

0.4

0.6

0.8

1.0

14.71.5 2.0 2.5 3.00.90

0.92

0.94

0.96

0.98

1.00

γγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγγ

ML, Phys. Rev. Lett. 118, 095301 (2017) Viewpoint: Yu. Shchadilova, Physics 10, 20 (2017)

Heavy molecules: strong-coupling (real deformation of the superfluid)

R. Schmidt and ML, Phys. Rev. X 6, 011012 (2016)

Light molecules: weak-coupling (rotational Lamb shift)

R. Schmidt and ML, Phys. Rev. Lett. 114, 203001 (2015)

Existence of angulons

(instead of expensive MC computations)

ML, Phys. Rev. Lett. 118, 095301 (2017) Viewpoint: Yu. Shchadilova, Physics 10, 20 (2017)

Existence of angulons

phenomenological parameters

(expressed through He properties, same for all molecules)

ML, Phys. Rev. Lett. 118, 095301 (2017) Viewpoint: Yu. Shchadilova, Physics 10, 20 (2017)

anisotropy of molecule-He potential (|| minus | ) —

Existence of angulons

phenomenological parameters

(expressed through He properties, same for all molecules)

ML, Phys. Rev. Lett. 118, 095301 (2017) Viewpoint: Yu. Shchadilova, Physics 10, 20 (2017)

Strong evidence thatangulons are formed in experiment

anisotropy of molecule-He potential (|| minus | ) —

Existence of angulons

Angulon instabilities

Explain ‘anomalous broadening’ in molecular spectra in He droplets

isotropic

0–0,0

0+0,0

1–1,0

1–0,1

anisotropic

Are those the angulon instabilities?

Douberly group, J. Phys. Chem. A 117, 11640 (2013)

Angulon instabilities

Douberly group, J. Phys. Chem. A 117, 11640 (2013) Vilesov group, Chem. Phys. Lett. 412, 176 (2005)

Igor Cherepanov

We have developed a theory for symmetric-top angulon I. Cherepanov and ML, Phys. Rev. Materials 1, 035602 (2017)

New emergent phenomena

E. Yakaboylu and ML, Phys. Rev. Lett. 118, 085302 (2017)

‘Anomalous screening’

Enderalp Yakaboylu

E. Yakaboylu, A. Deuchert, and ML, Phys. Rev. Lett. 119, 235301 (2017)

Non-Abelian magnetic monopoles

E. Yakaboylu, M. Shkolnikov, and ML, Phys. Rev. Lett., 121, 255302 (2018)

Quantum groups

Far from equilibrium dynamics of molecules in superfluid helium

Igor Cherepanov

Giacomo Bighin

I. Cherepanov, G. Bighin, L. Christiansen, A.V. Jørgensen, R. Schmidt, H. Stapelfeldt, ML, submitted (2019)

Posters

Far from equilibrium dynamics of molecules in helium

(also see PRL 118, 203203 (2017))

0.5

0.7

0.5

0.6

0.5

0.6

0.5

0.7

0.5

0.6

0.5

0.6

0.5

0.7

0.5

0.6

0.5

0.6

0.5

0.7

0.5

0.6

0.5

0.6

0 50 100 150 200 250 300 350

0.50.70.9

0.5

0.6

0.5

0.6

0.5

0.7

0.5

0.6

0.50.70.9

0.5

0.7

0.5

0.6

0.5

0.7

0.9

0.5

0.7

0 50 100 150 200 250 300 3500.50.60.7

0 100 200 300 400 500 600 7000.5

0.7

0.9

0 50 100 150 200 250 300 3500.5

0.7b3

b2

b1

d8

d7

d6

d5

d4

d3

d2

d1

c9

c8

c7

c6

c5

c4

c3

c2

c1

Experiment Laser pulse

14.2 J/cm2

7.1 J/cm2

14.2 J/cm2

5.0 J/cm2

2.8 J/cm2

2.1 J/cm2

1.4 J/cm2

5.0 J/cm2

1.1 J/cm2

Falign=0.7 J/cm2

14.2 J/cm2

10.6 J/cm2

7.1 J/cm2

5.0 J/cm2

2.8 J/cm2

1.4 J/cm2

1.1 J/cm2

0.7 J/cm2

Falign=0.4 J/cm2

OCS in helium droplets CS2 in helium droplets

I2 in gas phase

14.2 J/cm2

7.1 J/cm2

5.0 J/cm2

2.8 J/cm2

Falign=1.4 J/cm2

I2 in helium droplets

a1

a5

a3

a2

a4

t (ps)

Falign=1.4 J/cm2

t (ps)

t (ps)t (ps)

<cos

2 2

D>

1. “Equidistant band” of states

What is the physics behind it?

1. “Equidistant band” of states 2. Dynamical transfer of angular momentum

What is the physics behind it?

Igor Cherepanov

Giacomo Bighin

I. Cherepanov, G. Bighin, L. Christiansen, A.V. Jørgensen, R. Schmidt, H. Stapelfeldt, ML, submitted (2019)

Posters

Far from equilibrium dynamics of molecules in helium

(also see PRL 118, 203203 (2017))

0.5

0.7

0.5

0.6

0.5

0.6

0.5

0.7

0.5

0.6

0.5

0.6

0.5

0.7

0.5

0.6

0.5

0.6

0.5

0.7

0.5

0.6

0.5

0.6

0 50 100 150 200 250 300 350

0.50.70.9

0.5

0.6

0.5

0.6

0.5

0.7

0.5

0.6

0.50.70.9

0.5

0.7

0.5

0.6

0.5

0.7

0.9

0.5

0.7

0 50 100 150 200 250 300 3500.50.60.7

0 100 200 300 400 500 600 7000.5

0.7

0.9

0 50 100 150 200 250 300 3500.5

0.7b3

b2

b1

d8

d7

d6

d5

d4

d3

d2

d1

c9

c8

c7

c6

c5

c4

c3

c2

c1

Experiment Laser pulse

14.2 J/cm2

7.1 J/cm2

14.2 J/cm2

5.0 J/cm2

2.8 J/cm2

2.1 J/cm2

1.4 J/cm2

5.0 J/cm2

1.1 J/cm2

Falign=0.7 J/cm2

14.2 J/cm2

10.6 J/cm2

7.1 J/cm2

5.0 J/cm2

2.8 J/cm2

1.4 J/cm2

1.1 J/cm2

0.7 J/cm2

Falign=0.4 J/cm2

OCS in helium droplets CS2 in helium droplets

I2 in gas phase

14.2 J/cm2

7.1 J/cm2

5.0 J/cm2

2.8 J/cm2

Falign=1.4 J/cm2

I2 in helium droplets

a1

a5

a3

a2

a4

t (ps)

Falign=1.4 J/cm2

t (ps)

t (ps)t (ps)

<cos

2 2

D>

Igor Cherepanov

Giacomo Bighin

I. Cherepanov, G. Bighin, L. Christiansen, A.V. Jørgensen, R. Schmidt, H. Stapelfeldt, ML, submitted (2019)

Posters

Far from equilibrium dynamics of molecules in helium

(also see PRL 118, 203203 (2017))

0.5

0.7

0.5

0.6

0.5

0.6

0.5

0.7

0.5

0.6

0.5

0.6

0.5

0.7

0.5

0.6

0.5

0.6

0.5

0.7

0.5

0.6

0.5

0.6

0 50 100 150 200 250 300 350

0.50.70.9

0.5

0.6

0.5

0.6

0.5

0.7

0.5

0.6

0.50.70.9

0.5

0.7

0.5

0.6

0.5

0.7

0.9

0.5

0.7

0 50 100 150 200 250 300 3500.50.60.7

0 100 200 300 400 500 600 7000.5

0.7

0.9

0 50 100 150 200 250 300 3500.5

0.7(b3)

(b2)

(b1)

(d8)

(d7)

(d6)

(d5)

(d4)

(d3)

(d2)

(d1)

(c9)

(c8)

(c7)

(c6)

(c5)

(c4)

(c3)

(c2)

(c1)

Experiment Laser pulse Angulon theory

14.2 J/cm2

7.1 J/cm2

14.2 J/cm2

5.0 J/cm2

2.8 J/cm2

2.1 J/cm2

1.4 J/cm2

5.0 J/cm2

1.1 J/cm2

Falign=0.7 J/cm2

14.2 J/cm2

10.6 J/cm2

7.1 J/cm2

5.0 J/cm2

2.8 J/cm2

1.4 J/cm2

1.1 J/cm2

0.7 J/cm2

Falign=0.4 J/cm2

OCS in helium droplets CS2 in helium droplets

I2 in gas phase

14.2 J/cm2

7.1 J/cm2

5.0 J/cm2

2.8 J/cm2

Falign=1.4 J/cm2

I2 in helium droplets

(a1)

(a5)

(a3)

(a2)

(a4)

t (ps)

Falign=1.4 J/cm2

t (ps)

t (ps)t (ps)

<cos

2 2

D>

Angulons in 'real' solid state systems

Einstein-de Haas effect (1915) Ultrafast magnetism

Beaurepaire et al., PRL 1996

Spin-phonon relaxation and phonon spin Chudnovskii, Garanin PRL 2005; Niu, Zhang, PRL 2014;Garanin & Chudnovskii PRB 2015

Nano-magneto-mechanical systems Wernsdorfer group Nature Comm. 2016

Spin mechatronics Matsuo, Saitoh, and Maekawa Frontiers of physics 2015…and many many more

RU Nijmegen: Johan Mentink & Mikhail Katsnelson

Angulons in 'real' solid state systems

At every step

Compare to fully controlled experiments on molecules

Electron + phononsMolecule + helium

“Easy” “Hard”

Rotational angular momentum Orbital angular momentum

Superfluid excitations Lattice phonons

… …

Angulons in solids

Angulon Multi-orbital atom Phonon field

Total angular momentumSpin+orbital

angular momentum Phonon angular momentum

W. Rzadkowski and ML, J. Chem. Phys. 148, 104307 (2018)

Electron-phonon coupling

Landé g-factor increases

due to phonons

Experiments on OH molecules in He show exactly the same effect

(Douberly group, unpublished)

4

J. Mentink, M. I. Katsnelson, and ML, Phys. Rev. B 99, 064428 (2019)

Example: renormalisation of Landé g-factor

Summary• Our claim: angulons provide a general framework to study

angular momentum dynamics in quantum many particle systems

• We have shown: it works for molecules in superfluids

Tutorial chapter: ML, R. Schmidt, arXiv:1703.06753

Future directions• Many-body techniques for the angulon problem:

path integral, diagrammatic Monte Carlo, …G. Bighin and ML, Phys. Rev. B 96, 085410 (2017) G. Bighin, T. Tscherbul, and ML, Phys. Rev. Lett., 121, 165301 (2018)

Any ideas and suggestions are welcome!

• Applications to chemical reaction dynamics

• …

• Applications to transport in hybrid organic/inorganic perovskites

The group

Laleh Safari (IST fellow)

Jan Kaczmarczyk (IST fellow)

Bikash Midya (IST fellow)

Enderalp Yakaboylu (IST fellow)

Richard Schmidt (MPQ)

Xiang Li

Igor CherepanovGiacomo Bighin

Collaborations

Misha Katsnelson

Wojciech Rzadkowski

Henrik Stapelfeldt (Aarhus)

Mikhail Maslov

2017–2020 2019–2024

Andreas Deuchert Misha Shkolnikov

(RU Nijmegen)

(IST Austria)

Funding

Johan Mentink

Areg Ghazaryan (IST plus)

The group

Laleh Safari (IST fellow)

Jan Kaczmarczyk (IST fellow)

Bikash Midya (IST fellow)

Enderalp Yakaboylu (IST fellow)

Richard Schmidt (MPQ)

Xiang Li

Igor CherepanovGiacomo Bighin

Collaborations

Misha Katsnelson

Wojciech Rzadkowski

Henrik Stapelfeldt (Aarhus)

Mikhail Maslov

2017–2020 2019–2024

Andreas Deuchert Misha Shkolnikov

(RU Nijmegen)

(IST Austria)

Funding

Johan Mentink

Areg Ghazaryan (IST plus)

Don’t miss their posters!

Simple variational ansatz: single bath excitations only

angulonquantum

rotormany-body field

angular momentum conservationtotal angular momentum

The “angulon” quasiparticle

Spectrum of the angulon (an example)

Spectrum of the angulon (an example)

–15 –10 –5 0

–4

–2

0

2

4

6

8

ω

Log [ ]

1+1,0

1–1,0

0–0,0

1–0,1

2–1,1

3–2,12+

2,0

2–2,0

0+0,0

–1115555 ––11100

0 1 2 3 4 5A ( )ωL

22,0

11,0

00,0

Lj,Λ

~

~

~

n

The only good quantum number: total angular momentum L“Approximate” quantum numbers: angular momenta of molecule, j, and bosons, /\

density or coupling

Ene

rgy

in ro

tatio

nal c

onst

ants

R. Schmidt and ML, Phys. Rev. Lett. 114, 203001 (2015) R. Schmidt and ML, Phys. Rev. X 6, 011012 (2016)

1. For different L, the energies change differently

Rotational Lamb shift due to the boson field

–15 –10 –5 0

–4

–2

0

2

4

6

8

ω

Log [ ]

1+1,0

1–1,0

0–0,0

1–0,1

2–1,1

3–2,12+

2,0

2–2,0

0+0,0

–1115555 ––11100

0 1 2 3 4 5A ( )ωL

22,0

11,0

00,0

Lj,Λ

~

~

~

ndensity or coupling

Ene

rgy

in ro

tatio

nal c

onst

ants

R. Schmidt and ML, Phys. Rev. Lett. 114, 203001 (2015) R. Schmidt and ML, Phys. Rev. X 6, 011012 (2016)

–15 –10 –5 0

–4

–2

0

2

4

6

8

ω

Log [ ]

1+1,0

1–1,0

0–0,0

1–0,1

2–1,1

3–2,12+

2,0

2–2,0

0+0,0

–1115555 ––11100

0 1 2 3 4 5A ( )ωL

22,0

11,0

00,0

Lj,Λ

~

~

~

n

2. There are splittings of rotational lines

Let’s zoom in…

density or coupling

Ene

rgy

in ro

tatio

nal c

onst

ants

R. Schmidt and ML, Phys. Rev. Lett. 114, 203001 (2015) R. Schmidt and ML, Phys. Rev. X 6, 011012 (2016)

Angulon Fine Structure

isotropic

0–0,0

0+0,0

1–1,0

1–0,1

anisotropic

Phonon wing (isotropic impurity-boson interactions) Splitting between |j=L, no phonons> and |j=L, 1 phonon with >

‘Angulon instabilities’ (anisotropic impurity-boson interactions)Splitting between |j=L, no phonons> and |j=L–1, 1 phonon with >

λ = 0

λ = 1

R. Schmidt and ML, Phys. Rev. Lett. 114, 203001 (2015) R. Schmidt and ML, Phys. Rev. X 6, 011012 (2016)

The canonical transformation

Bosons: laboratory frame (x, y, z)

Molecule: rotating frame (x’, y’, z’),

defined by Euler angles

z

x

y

z ( ,̂ ˆ)

y

x

γ̂

xxxx xx

yx

yy

γγ̂̂

y

Bosons: laboratory frame (x, y, z)z

x

y

z ( ,̂ ˆ)

y

x

γ̂

xxxx xx

yx

yy

γγ̂̂

y

With the total angular momentum of bosons

angular momentum matrices

Molecule: rotating frame (x’, y’, z’),

defined by Euler angles

The canonical transformation

Transformed Hamiltonian

Why is it better?1. It does not contain the molecular coordinates (angles)

Original H: coupling mixes 3D angular momenta, leading to 3jn-symbols

Transformed H: coupling ~ (as e.g. in spin-orbit interaction)

Addition of 3D angular momenta is replaced by addition of “spins”

R. Schmidt and ML, Phys. Rev. X 6, 011012 (2016)

2. The transformation singles out total angular momentum, , , the only conserved quantity of the problem

Why is it better?

Transformed Hamiltonian

R. Schmidt and ML, Phys. Rev. X 6, 011012 (2016)

Why is it better?

3. In the regime of B=0, H can be diagonalized exactly:

Thus, one can look for perturbative solutions near the state which already contains an infinite number of phonon excitations:

Transformed Hamiltonian

R. Schmidt and ML, Phys. Rev. X 6, 011012 (2016)