Molecular impurities interacting with a many-body environment: - PowerPoint PPT Presentation

Molecular impurities interacting with a many-body environment: dynamics in Helium nanodroplets G. Bighin and M. Lemeshko Institute of Science and Technology Austria SuperFluctuations 2018 – San Benedetto del Tronto, September 6th, 2018

Quantum impurities Definition: one (or a few particles) interacting with a many-body environment. How are the properties of the particle modified by the interaction? 2/19 O ( 10 23 ) degrees of freedom.

From impurities to quasiparticles Structureless impurity: translational degrees of freedom/linear momentum exchange with the bath. Most common cases: electron in a solid, atomic impurities in a BEC. Image from: F. Chevy, Physics 9 , 86. Composite impurity: translational and internal (i.e. rotational) degrees of freedom/linear and angular momentum exchange. 3/19

From impurities to quasiparticles Structureless impurity: translational degrees of freedom/linear momentum exchange with the bath. atomic impurities in a BEC. Image from: F. Chevy, Physics 9 , 86. Composite impurity: translational and internal (i.e. rotational) degrees of freedom/linear and angular momentum exchange. 3/19 Most common cases: electron in a solid,

From impurities to quasiparticles Structureless impurity: translational degrees of freedom/linear momentum exchange with the bath. Most common cases: electron in a solid, atomic impurities in a BEC. Image from: F. Chevy, Physics 9 , 86. Composite impurity: translational and internal (i.e. rotational) degrees of freedom/linear and angular momentum exchange. 3/19

From impurities to quasiparticles Structureless impurity: translational degrees of freedom/linear momentum exchange with the bath. Most common cases: electron in a solid, atomic impurities in a BEC. Image from: F. Chevy, Physics 9 , 86. Composite impurity: translational and internal (i.e. rotational) degrees of freedom/linear and angular momentum exchange. 3/19 This scenario (with a bosonic bath) can be for- laron and the Fröhlich Hamiltonian. malized in terms of quasiparticles using the po-

From impurities to quasiparticles Structureless impurity: translational degrees of freedom/linear momentum exchange with the bath. Most common cases: electron in a solid, atomic impurities in a BEC. Image from: F. Chevy, Physics 9 , 86. Composite impurity: translational and internal (i.e. rotational) degrees of freedom/linear and angular momentum exchange. 3/19 This scenario (with a bosonic bath) can be for- laron and the Fröhlich Hamiltonian. malized in terms of quasiparticles using the po-

From impurities to quasiparticles Structureless impurity: translational cle? The main difgiculty: the non-Abelian SO(3) rotating counterpart of the polaron quasiparti- What about a rotating particle? Can there be a laron and the Fröhlich Hamiltonian. This scenario (with a bosonic bath) can be for- 3/19 angular momentum exchange. (i.e. rotational) degrees of freedom/linear and Composite impurity: translational and internal Image from: F. Chevy, Physics 9 , 86. atomic impurities in a BEC. Most common cases: electron in a solid, exchange with the bath. degrees of freedom/linear momentum malized in terms of quasiparticles using the po- algebra describing rotations.

The angulon phonons 4 Y. Shchadilova, ”Viewpoint: A New Angle on Quantum Impurities” , Physics 10 , 20 (2017). 3 M. Lemeshko, Phys. Rev. Lett. 118 , 095301 (2017). 2 R. Schmidt and M. Lemeshko, Phys. Rev. X 6 , 011012 (2016). 1 R. Schmidt and M. Lemeshko, Phys. Rev. Lett. 114 , 203001 (2015). bath 3 . molecule in any kind of bosonic • Phenomenological model for a weakly-interacting BEC 1 . • Derived rigorously for a molecule in a • Linear molecule. molecule-phonon interaction A composite impurity in a bosonic environment can be described by the 4/19 J 2 molecule angulon Hamiltonian 1 , 2 , 3 , 4 (angular momentum basis: k → { k , λ, µ } ): [ ] ∑ ∑ ω k ˆ k λµ ˆ λµ (ˆ θ, ˆ ϕ )ˆ k λµ + Y λµ (ˆ θ, ˆ ϕ )ˆ ˆ B ˆ b † Y ∗ b † H = + + U λ ( k ) b k λµ b k λµ ���� k λµ k λµ � �� � � �� �

The angulon phonons 4 Y. Shchadilova, ”Viewpoint: A New Angle on Quantum Impurities” , Physics 10 , 20 (2017). 3 M. Lemeshko, Phys. Rev. Lett. 118 , 095301 (2017). 2 R. Schmidt and M. Lemeshko, Phys. Rev. X 6 , 011012 (2016). 1 R. Schmidt and M. Lemeshko, Phys. Rev. Lett. 114 , 203001 (2015). part. symmetric part. bath 3 . molecule in any kind of bosonic • Phenomenological model for a weakly-interacting BEC 1 . • Derived rigorously for a molecule in a • Linear molecule. molecule-phonon interaction A composite impurity in a bosonic environment can be described by the 4/19 J 2 molecule angulon Hamiltonian 1 , 2 , 3 , 4 (angular momentum basis: k → { k , λ, µ } ): [ ] ∑ ∑ ω k ˆ k λµ ˆ λµ (ˆ θ, ˆ ϕ )ˆ k λµ + Y λµ (ˆ θ, ˆ ϕ )ˆ ˆ B ˆ b † Y ∗ b † H = + + U λ ( k ) b k λµ b k λµ ���� k λµ k λµ � �� � � �� � λ = 0: spherically λ ≥ 1 anisotropic

‘cage’ in perovskites. from the electrons to a crystal • Molecules embedded into Composite impurities: where to find them Strong motivation for the study of composite impurities comes from many difgerent fields. Composite impurities are realized as: • Ultracold molecules and ions. • Rotating molecules inside a • Angular momentum transfer lattice. helium nanodroplets. B. Midya, M. Tomza, R. Schmidt, and M. Lemeshko, Phys. Rev. A 94 , 041601(R) (2016). 5/19

from the electrons to a crystal • Molecules embedded into Composite impurities: where to find them Strong motivation for the study of composite impurities comes from many difgerent fields. Composite impurities are realized as: • Ultracold molecules and ions. • Rotating molecules inside a • Angular momentum transfer lattice. helium nanodroplets. T. Chen et al., PNAS 114 , 7519 (2017). J. Lahnsteiner et al., Phys. Rev. B 94 , 214114 (2016). Image from: C. Eames et al, Nat. Comm. 6 , 7497 (2015). 5/19 ‘cage’ in perovskites.

• Molecules embedded into Composite impurities: where to find them Strong motivation for the study of composite impurities comes from many difgerent fields. Composite impurities are realized as: • Ultracold molecules and ions. • Rotating molecules inside a • Angular momentum transfer lattice. helium nanodroplets. J.H. Mentink, M.I. Katsnelson, M. Lemeshko, “Quantum many-body dynamics of the Einstein-de Haas efgect” , arXiv:1802.01638 5/19 ‘cage’ in perovskites. from the electrons to a crystal

Composite impurities: where to find them Strong motivation for the study of composite impurities comes from many difgerent fields. Composite impurities are realized as: • Ultracold molecules and ions. • Rotating molecules inside a • Angular momentum transfer lattice. • Molecules embedded into helium nanodroplets. Image from: J. P. Toennies and A. F. Vilesov, Angew. Chem. Int. Ed. 43 , 2622 (2004). 5/19 ‘cage’ in perovskites. from the electrons to a crystal

Out-of-equilibrium dynamics of molecules in He nanodroplets

in 4 He Dynamical alignment of molecules in He nanodroplets Molecules embedded into helium nanodroplets: Gas phase (free) Images from: J. P. Toennies and A. F. Vilesov, Angew. Chem. Int. Ed. 43 , 2622 (2004). 6/19

Dynamical alignment of molecules in He nanodroplets Molecules embedded into helium nanodroplets: Gas phase (free) Images from: J. P. Toennies and A. F. Vilesov, Angew. Chem. Int. Ed. 43 , 2622 (2004). 6/19 in 4 He

in 4 He Dynamical alignment of molecules in He nanodroplets Molecules embedded into helium nanodroplets: Gas phase (free) Images from: J. P. Toennies and A. F. Vilesov, Angew. Chem. Int. Ed. 43 , 2622 (2004). Rotational spec- trum Renormalizated lines (smaller efgec- tive B ) 6/19

Dynamical alignment of molecules in He nanodroplets pulses, one gets 118 , 203203 (2017). Image from B. Shepperson et al., Phys. Rev. Lett. with: Dynamical alignment experiments: 7/19 alignment as a function of time. and varying the time between the two • Fragments are imaged, reconstructing • Averaging over multiple realizations, • Kick pulse, aligning the molecule. • Probe pulse, destroying the molecule. ⟨ ⟩ cos 2 ˆ θ 2D ( t ) cos 2 ˆ θ cos 2 ˆ θ 2D ≡ θ + sin 2 ˆ θ sin 2 ˆ cos 2 ˆ ϕ

Dynamical alignment of molecules in He nanodroplets Interaction of a free molecule with an ofg-resonant laser pulse G. Kaya, Appl. Phys. B 6 , 122 (2016). Movie 8/19 J 2 − 1 4 ∆ α E 2 ( t ) cos 2 ˆ ˆ H = B ˆ θ When acting on a free molecule, the laser excites in a short time many rotational states ( L ↔ L + 2), creating a rotational wave packet:

Dynamical alignment of molecules in He nanodroplets understanding. Monte Carlo? Efgect of the environment is substantial: free molecule vs. same molecule in He . 9/19 Not even a qualitative Stapelfeldt group, Phys. Rev. Lett. 110 , 093002 (2013). n g p l i o u g c o n t r — S c s m i n a d y m u b r i u i l i e q f - t - o O u — ∼ T ) k B ( B r e t u e r a m p e e t n i t F i —