Quantum Optics Group (LMU) - Quantum Many Body Systems Division (MPQ)

A Lithium Quantum Gas Microscope

Ultracold atoms in optical lattices have proven to be a powerful tool to study quantum many-body systems. Recent experiments have demonstrated the potential of single-site resolved detection in optical lattices for the study of strongly correlated bosonic systems. In our experiment we plan to apply similar techniques to fermions. We use spin mixtures of Lithium-6 atoms to produce a degenerate fermionic many-body system trapped in an 3D optical lattice with a lattice spacing of about 1.2 μm. With a high resolution imaging system, we will be able to resolve single sites in a 2D plane of the lattice and image single atoms. We plan to superpose an additional small-scale pinning lattice onto the larger-scale physics lattice in order to freeze out the distribution of atoms during imaging. Doing so, we separate the physics lattice from the "detector" which adds flexibility to the system, for example, the momentum distribution of the atoms could also be measured. As a first application we plan to study the quantum phases of the Fermi-Hubbard Hamiltonian locally where we concentrate on the study of spin correlations in the system.

Experimental setup

The picture shows our cavity enhanced frequency doubling stage to generate 323nm light.

We heat a block (approx. 2x2cm) of the fermionic Lithium-6 isotope to 350 degree centigrade in an oven, generating an atomic beam out of a small aperture. A standard decreasing-field Zeeman slower decelerates the atoms, which are then captured and cooled in a Magneto-Optical Trap (MOT) operating at 671nm in a steel octagon chamber. At this stage we end up with 109 atoms at a temperature of about 300 μK.  Next, a second MOT is switched on operating at the narrow 2S1/2 ↔ 3P3/2 transition at 323nm. After this UV cooling stage we end up with ~5*108 atoms at roughly 70 μK. The UV light is provided by a home build laser system using two nonlinear frequency conversions. The UV MOT also enables the direct loading of an optical dipole trap at a magic wavelength close to 1070nm, where the relative light-shift of the transition vanishes. Using a large volume high power dipole trap we capture a 10 million cold atoms from the UV MOT. A second, more tightly focused dipole trap at 1064nm is switched on afterwards, to transport the atoms from the MOT chamber into the main glass cell. This is achieved by mechanically moving the focus of the 1064nm beam. At the final position, the transport trap is crossed with another trapping beam to increase the density and allow for efficient evaporative cooling to degeneracy in a Feshbach field.

Optical Lattice Generation

1D scheme illustrating the setup for the generation of 2 parallel beam pairs with a certain distance to the optical axis.
Beam pattern entering the objective (left) and the corresponding intensity distribution in the focal plane (right).

After the final evaporation the degenerate sample of atoms is loaded to the optical lattice. The lattice is produced via an interferometric projection method. A modified Michelson interferometer generates pairs of phase coherent, parallel beams which are sent through the high resolution objective (NA=0.5, ~1 μm resolution at 670nm). The objective transforms the spatial offset from the optical axis of the incoming beams into an angle under which the beams intersect at the focal position. Four pairs of beams (each pair is phase coherent) are sent through the objective such that we obtain two 2D optical lattices. We choose the beam separation such that a 2D superlattice is generated at the position of the atoms. Using a similar interferometer setup, we project another set of beams from the side to generate a superlattice along the vertical direction. 

Recent Publications

Imaging magnetic polarons in the doped Fermi-Hubbard model

Polarons are among the most fundamental quasiparticles emerging in interacting many-body systems, forming already at the level of a single mobile dopant. In the context of the two- dimensional Fermi-Hubbard model, such polarons are predicted to form around charged dopants in an antiferromagnetic background in the low doping regime close to the Mott insulating state. Macroscopic transport and spectroscopy measurements related to high-Tc materials have yielded strong evidence for the existence of such quasiparticles in these systems. Here we report the first microscopic observation of magnetic polarons in a doped Fermi-Hubbard system, harnessing the full single-site spin and density resolution of our ultracold-atom quantum simulator. We reveal the dressing of mobile doublons by a local reduction and even sign reversal of magnetic correlations, originating from the competition between kinetic and magnetic energy in the system. The experimentally observed polaron signatures are found to be consistent with an effective string model at finite temperature. We demonstrate that delocalization of the doublon is a necessary condition for polaron formation by contrasting this mobile setting to a scenario where the doublon is pinned to a lattice site.

For more detailed information see our publication: 


Direct observation of incommensurate magnetism in Hubbard chains

One dimensional quantum many-body systems are paradigmatic examples of the breakdown of Landau Fermi liquid theory, where interacting systems are effectively described by non-interacting quasiparticles with the same quantum numbers albeit with renormalized properties. A universal description of gapless 1D systems is provided by Luttinger liquid theory, which describes the low energy properties of the doped Hubbard model. Quantum gas microscopes allow to test this description with a resolution down to a single particle and spin and to perform controlled studies of the dimensional crossover from 1D to 2D where much less is know.

Owing to our access to all local degrees of freedom, we directly observed here two fundamental predictions for Luttinger liquids. First we detected a linear variation of the spin-density wave vector as a function of doping in good agreement with quantum Monte-Carlo calculations at T/t=0.29. The microscopic origin of this phenomenon was attributed to the dilution of antiferromagnetic correlations by holes and doublons acting as domain walls. Second, when studying spin-imbalanced clouds in squeezed space, we observed a linear increase of the spin-density wave vector with polarization in excellent agreement with the exact diagonalization calculations of the Heisenberg model averaged over our experimental spin and atom number distributions. This wavelength extension was microscopically attributed to pairs of parallel spins acting as domain walls for the antiferromagnetic order. Finally, when inducing interchain coupling to map out spin correlations in the crossover regime, we observed fundamentally different spin correlations in the direct vicinity of doublons in 2D, suggesting the formation of a magnetic polaron.

For more detailed information see our publication:


Revealing hidden antiferromagnetic correlations in doped Hubbard chains via string correlators

The characterization of phases of matter usually requires the measurement of two-point correlations. Whereas these allow to detect symmetry broken phases such as Bose-Einstein condensates or antiferromagnets, they fail to capture more exotic correlations appearing in topological phases or spin-charge separated systems.There, one needs to perform a measurement over an extensive part of the system, simultaneously measuring all the spins in a spin-1 antiferromagnetic chain for example, to reveal the underlying order.

In this work, we used spin-resolved quantum gas microscopy to study equilibrium signatures of spin-charge separation in hole-doped Hubbard chains. We observed that a single hole acts as a domain wall for the antiferromagnetic ordering whose delocalization supresses spin correlations compared to the half-filled case. Owing to spin-charge separation, the underlying spin correlations are just "hidden", similar to the one in the Haldane phase of spin-1 antiferromagnetic chains. These can be detected either using a non-local string correlator or by evaluating spin correlations directly in squeezed space, defined by removing holes from the chain in the analysis. We directly evaluated these non-local correlations by simultaneoulsy measuring the spin and occupation on each site of the optical lattice to reveal the asymptotic wave function factorization predicted by Woynarovitch, Ogata and Shiba in the 80's.These results constitute a static picture of spin-charge separation complementary to the dynamic signatures usually discussed in traditional condensed matter systems.

 For more detailed information see our publication:


Spin and density resolved quantum gas microscopy of antiferromagnetic correlations in Hubbard chains

We were able to investigate interacting two component fermi gases which were loaded into optical lattices in one and two dimensional systems. By applying a combination of optical superlattice potentials and magnetic field gradients we are able to resolve not only the lattice occupation but also the spins of the atoms. Using the power of a quantum gas microscope we could select the 1 dimensional Hubbard chains in the inner region of the clouds showing the lowest entropies. Investigation of correlations in these inner chains showed antiferromagnetic correlations up to distances of three lattice sites. Following the correlations we were able to extract entropies of the system as low as s= 0.4 kB

The publication is now published in Science


Microscopic Observation of Pauli Blocking in Degenerate Fermionic Lattice Gases

After the selection of a single vertical lattice plane of atoms placed in the focus of the high NA objective we load the atoms into a 2D lattice which we produce as described in the former section.

In case of a spin polarized atomic sample which we load in absence of any interaction between the atoms into a simple 2D lattice we observe the formation of a band insulating state.  Due to the fundamental principle of Pauli blocking between fermions particle number fluctuations get strongly suppressed. Choosing the right ratio between the total number of particles and the confinement we observe an average particle number of one on each lattice site. Due to the ability of single atom sensitive detection we are able to perform thermometry and extract local as well as global thermodynamic quantities. For more detailed information see our publication: