Tilman Enss group | Ruprecht-Karls-Universität Heidelberg
Dr. Nicolò Defenu (Postdoc)
Former students and team members
M.Sc. Moritz Drescher (PhD student)
B.Sc. Hans Böhringer (Master student)
Andrea Colcelli (visiting PhD student)
M.Sc. Volker Karle (Heidelberg 2018: Binary Bose mixtures in 2D)
M.Sc. Martin Braß (Heidelberg 2017: Phase
transitions and stability in resonant Bose-Fermi mixtures)
M.Sc. Sergej Trenkenschu (Heidelberg 2017: Quench dynamics
of a Fermi gas)
B.Sc. Dominik Lorenz (Heidelberg 2016: Quench dynamics in the
B.Sc. Daniel Issing (Heidelberg 2015: Bethe ansatz and
quench dynamics for 1D integrable quantum systems)
B.Sc. Bruno Faigle-Cedzich (Heidelberg 2015: Shear
viscosity of two-component Fermi gas)
My research focuses on many-body theory, mainly dynamics and
transport in strongly correlated quantum systems, ranging from
ultracold atomic gases to superconductors and quantum wires.
I work on the development of several modern and advanced
theoretical tools including the functional renormalization group
(fRG), Hamiltonian flows, Luttinger-Ward calculations, transfer-matrix DMRG and the newly developed
articles on Google Scholar
- Quench dynamics in 1d chains and Many-body localization (MBL), using
the Lightcone renormalization group
- Many-body dynamics and transport in interacting ultracold atomic gases
- Quantum critical behavior in disordered correlated electron systems
- Nonequilibrium dynamics and transport in quantum dots and Luttinger liquids
- Raman and optical spectroscopy in cuprates
- Functional renormalization group method (fRG)
- Aging behavior in stochastic systems without detailed balance
Isolated quantum systems and universality under extreme conditions,
Dynamical criticality and domain-wall coupling in long-range Hamiltonians
Dynamical quantum phase transitions hold a deep connection to the
underlying equilibrium physics of the quench Hamiltonian. In a
recent study [J.~C.~Halimeh et al., arXiv:1810.07187], it has been numerically demonstrated that the appearance of anomalous cusps in the Loschmidt return rate coincides with the presence of bound domain walls in the spectrum of the quench Hamiltonian. Here, we consider transverse-field Ising chains with power-law and exponentially decaying interactions, and show that by removing domain-wall coupling via a truncated Jordan-Wigner transformation onto a Kitaev chain with long-range hopping and pairing, anomalous dynamical criticality is no longer present. This indicates that bound domain walls are necessary for anomalous cusps to appear in the Loschmidt return rate. We also calculate the dynamical phase diagram of the Kitaev chain with long-range hopping and pairing, which in the case of power-law couplings is shown to exhibit rich dynamical criticality including a doubly critical dynamical phase.
N. Defenu, T. Enss, and J.C. Halimeh,
Real-space dynamics of attractive and repulsive polarons in Bose-Einstein condensates
We investigate the formation of a Bose polaron when a single
impurity in a Bose-Einstein condensate is quenched from a
non-interacting to an attractively interacting state in the vicinity
of a Feshbach resonance. We use a beyond-Fröhlich Hamiltonian
to describe both sides of the resonance and a coherent-state
variational ansatz to compute the time evolution of boson density
profiles in position space. We find that on the repulsive side of
the Feshbach resonance, the Bose polaron performs long-lived
oscillations, which is surprising given that the two-body problem
has only one bound state coupled to a continuum. They arise due to
interference between multiply occupied bound states and therefore
can be only found with many-body approaches such as the
coherent-state ansatz. Furthermore, an impurity
introduced at non-zero velocity on the repulsive
side is periodically slowed down or even arrested before
speeding up again.
M. Drescher, M. Salmhofer, and T. Enss,
Phys. Rev. A 99, 023601 (2019).
Universal Spin Transport and Quantum Bounds for Unitary Fermions
We review recent advances in experimental and theoretical understanding of spin transport in strongly interacting Fermi gases. The central new phenomenon is the observation of a lower bound on the (bare) spin diffusivity in the strongly interacting regime. Transport bounds are of broad interest for the condensed matter community, with a conceptual similarity to observed bounds in shear viscosity and charge conductivity. We discuss the formalism of spin hydrodynamics, how dynamics are parameterized by transport coefficients, the effect of confinement, the role of scale invariance, the quasi-particle picture, and quantum critical transport. We conclude by highlighting open questions, such as precise theoretical bounds, relevance to other phases of matter, and extensions to lattice systems.
T. Enss and J. H. Thywissen,
invited review for Annu. Rev. Condens. Matter Phys. 10, 85-106 (2019).
Quantum scale anomaly and spatial coherence in a 2D Fermi superfluid
Quantum anomalies are violations of classical scaling symmetries caused by quantum fluctuations. Although they appear prominently in quantum field theory to regularize divergent physical quantities, their influence on experimental observables is difficult to discern. Here, we discovered a striking manifestation of a quantum anomaly in the momentum-space dynamics of a 2D Fermi superfluid of ultracold atoms. We measured the position and pair momentum distribution of the superfluid during a breathing mode cycle for different interaction strengths across the BEC-BCS crossover. Whereas the system exhibits self-similar evolution in the weakly interacting BEC and BCS limits, we found a violation in the strongly interacting regime. The signature of scale-invariance breaking is enhanced in the first-order coherence function. In particular, the power-law exponents that characterize long-range phase correlations in the system are modified due to this effect, indicating that the quantum anomaly has a significant influence on the critical properties of 2D superfluids.
P. A. Murthy, N. Defenu, L. Bayha, M. Holten, P. M. Preiss, T. Enss, and S. Jochim,
High-temperature pairing in a strongly interacting two-dimensional Fermi gas
The nature of the normal phase of strongly correlated fermionic systems is an outstanding question in quantum many-body physics. We use spatially resolved radio-frequency spectroscopy to measure pairing energy of fermions across a wide range of temperatures and interaction strengths in a two-dimensional gas of ultracold fermionic atoms. We observed many-body pairing at temperatures far above the critical temperature for superfluidity. In the strongly interacting regime, the pairing energy in the normal phase considerably exceeds the intrinsic two-body binding energy of the system and shows a clear dependence on local density. This implies that pairing in this regime is driven by many-body correlations, rather than two-body physics. Our findings show that pairing correlations in strongly interacting two-dimensional fermionic systems are remarkably robust against thermal fluctuations.
A. Murthy, Mathias Neidig, Ralf Klemt, Luca Bayha, Igor Boettcher,
Tilman Enss, Marvin Holten, Gerhard Zürn, Philipp M. Preiss,
and Selim Jochim,
Science 359, 452-455 (2018).
Exploring the ferromagnetic behaviour of a repulsive Fermi gas through spin dynamics
Ferromagnetism is a manifestation of strong repulsive interactions between itinerant fermions in condensed matter. Whether short-ranged repulsion alone is sufficient to stabilize ferromagnetic correlations in the absence of other effects, such as peculiar band dispersions or orbital couplings, is, however, unclear. Here, we investigate ferromagnetism in the minimal framework of an ultracold Fermi gas with short-range repulsive interactions tuned via a Feshbach resonance...
F. Scazza, A. Amico, A. Burchianti, A. Recati, T. Enss, M. Inguscio,
M. Zaccanti, and G. Roati,
Nature Phys. 13, 704
Observation of quantum-limited spin transport in strongly interacting two-dimensional Fermi gases
We measure the transport and thermodynamic properties of two-dimensional ultracold Fermi gases through their demagnetization in a magnetic field gradient. Using a phase-coherent spin-echo sequence, we are able to distinguish bare spin diffusion from the Leggett-Rice effect, in which demagnetization is slowed by the precession of spin current around the local magnetization. When the two-dimensional scattering length is comparable to the inverse Fermi wave vector, we find that the bare transverse spin diffusivity reaches a minimum of 1.7(6)ℏ/m...
S. Smale, F. Böttcher, H. Sharum, B. A. Olsen, S. Trotzky,
T. Enss, and J. H. Thywissen,
Phys. Rev. Lett. 118, 130405 (2017).
slides of talk in Trieste, 2017.
We report the experimental measurement of the equation of state of a two-dimensional Fermi gas with attractive s-wave interactions throughout the crossover from a weakly coupled Fermi gas to a Bose gas of tightly bound dimers as the interaction strength is varied. We demonstrate that interactions lead to a renormalization of the density of the Fermi gas by several orders of magnitude. We compare our data near the ground state and at finite temperature with predictions for both fermions and bosons from quantum Monte Carlo simulations and Luttinger-Ward theory. Our results serve as input for investigations of close-to-equilibrium dynamics and transport in the two-dimensional system.
L. Bayha, D. Kedar, P. A. Murthy, M. Neidig, M. G. Ries, A. N. Wenz,
G. Zürn, S. Jochim, and T. Enss,
Phys. Rev. Lett. 116,
Viewpoint in Physics:
Journey from Classical to Quantum in Two Dimensions, by Meera
Atome in zwei Dimensionen (popular article in German, Phys. Unserer Zeit 47, 113 (2016)).
Nonlinear spin diffusion and spin rotation in a trapped Fermi gas
Transverse spin diffusion in a polarized, interacting Fermi gas leads to the Leggett-Rice effect, where the spin current precesses around the local magnetization. With a spin-echo sequence both the transverse diffusivity and the spin-rotation parameter γ are obtained; the sign of γ reveals the repulsive or attractive character of the effective interaction. In a trapped Fermi gas the spin diffusion equations become nonlinear, and their numerical solution exhibits an inhomogeneous spin state even at the spin echo time. While the microscopic diffusivity and γ increase at weak coupling, their apparent values inferred from the trap-averaged magnetization saturate in agreement with a recent experiment for a dilute ultracold Fermi gas.
Tilman Enss, Phys. Rev. A 91, 023614 (2015).
Observation of the Leggett-Rice effect in a unitary Fermi
PRL Editors' suggestion
We observe that the diffusive spin current in a strongly interacting degenerate Fermi gas of 40K precesses about the local magnetization. As predicted by Leggett and Rice, precession is observed both in the Ramsey phase of a spin-echo sequence, and in the nonlinearity of the magnetization decay. At unitarity, we measure a Leggett-Rice parameter γ=1.08(9) and a bare transverse spin diffusivity D0⊥
=2.3(4)ℏ/m for a normal-state gas initialized with full polarization and at one fifth of the Fermi temperature, where m is the atomic mass. For a unitary gas, γ→0 as temperature is increased to the Fermi temperature. Tuning the scattering length a, we find that a sign change in γ occurs in the range 0<(kFa)-1
≤1.3, where kF is the Fermi momentum. We discuss how γ reveals the effective interaction strength of the gas, such that a change in γ indicates a switching of branch, between a repulsive and an attractive Fermi gas.
S. Trotzky, S. Beattie, C. Luciuk, S. Smale, A. B. Bardon, T. Enss,
E. Taylor, S. Zhang, and J. H. Thywissen,
Phys. Rev. Lett. 114, 015301 (2015).
Purification and many-body localization in cold atomic gases
We propose to observe many-body localization in cold atomic gases by realizing a Bose-Hubbard chain with binary disorder and studying its non-equilibrium dynamics. In particular, we show that measuring the difference in occupation between even and odd sites, starting from a prepared density-wave state, provides clear signatures of localization. As hallmarks of the many-body localized phase we confirm, furthermore, a logarithmic increase of the entanglement entropy in time and Poissonian level statistics. Our numerical density-matrix renormalization group calculations for infinite system size are based on a purification approach which allows to perform the disorder average exactly, thus producing data without any statistical noise, and with maximal simulation times of up to a factor 10 longer than in the clean case.
Felix Andraschko, Tilman Enss, and Jesko Sirker, Phys. Rev. Lett. 113, 217201 (2014).
Universal equation of state and pseudogap in the two-dimensional Fermi gas
We determine the thermodynamic properties and the spectral function for a homogeneous two- dimensional Fermi gas in the normal state using the Luttinger-Ward, or self-consistent T-matrix, approach. The density equation of state deviates strongly from that of the ideal Fermi gas even for moderate interactions, and our calculations suggest that temperature has a pronounced effect on the pressure in the crossover from weak to strong coupling, consistent with recent experiments. We also compute the superfluid transition temperature for a finite system in the crossover region. There is a pronounced pseudogap regime above the transition temperature: the spectral function shows a Bogoliubov-like dispersion with backbending, and the density of states is significantly suppressed near the chemical potential. The contact density at low temperatures increases with interaction and compares well with both experiment and zero-temperature Monte Carlo results.
Marianne Bauer, Meera M. Parish, and Tilman Enss, Phys. Rev. Lett. 112, 135302 (2014).
Damping of the quadrupole mode in a two-dimensional Fermi gas
In a recent experiment [E. Vogt et al., Phys. Rev. Lett. 108, 070404 (2012)], quadrupole and breathing modes of a two-dimensional Fermi gas were studied. We model these collective modes by solving the Boltzmann equation via the method of phase-space moments up to fourth order, including in-medium effects on the scattering cross section. In our analysis, we use a realistic Gaussian potential deformed by the presence of gravity and magnetic field gradients. We conclude that the origin of the experimentally observed damping of the quadrupole mode, especially in the weakly interacting (or even non-interacting) case, cannot be explained by these mechanisms.
Silvia Chiacchiera, Dany Davesne, Tilman Enss, and Michael Urban, Phys. Rev. A 88, 053616 (2013).
M. Urban, S. Chiacchiera, D. Davesne,
T. Enss, and P.-A. Pantel, J. Phys.: Conf. Ser. 497, 012028 (2014).
Quantum critical transport in the unitary Fermi gas
The thermodynamic and transport properties of the unitary Fermi gas
at finite temperature T are governed by a quantum critical point at
T=0 and zero density. We compute the universal shear viscosity to
entropy ratio η/s in the high-temperature quantum critical regime
T≫|μ| and find that this strongly coupled quantum fluid comes
close to perfect fluidity η/s=ℏ/4πkB
. Using a
controlled large-N expansion we show that already at the first
non-trivial order the equation of state and the Tan contact density
C agree well with the most recent experimental measurements and
theoretical Luttinger-Ward and Bold Diagrammatic Monte Carlo
Enss, Phys. Rev. A 86, 013616 (2012).
talk at ERG 2012 conference
Enss, Büro für Denkmalforschung und Denkmalpflege
Excitation spectra and rf-response near the polaron-to-molecule
transition from the functional renormalization group
A light impurity in a Fermi sea undergoes a transition from a
polaron to a molecule for increasing interaction. We develop a
new method to compute the spectral functions of the polaron
and molecule in a unified framework based on the functional
renormalization group with full self-energy feedback. We
discuss the energy spectra and decay widths of the attractive
and repulsive polaron branches as well as the molecular bound
state and confirm the scaling of the excited state decay rate
near the transition. The quasi-particle weight of the polaron
shifts from the attractive to the repulsive branch across the
transition, while the molecular bound state has a very small
residue characteristic for a composite particle. We propose an
experimental procedure to measure the repulsive branch in a
Li6 Fermi gas using rf-spectroscopy and calculate the
Richard Schmidt and Tilman Enss, Phys. Rev. A 83, 063620 (2011)
slides of talk
at ERG 2014 conference