Random Unitaries in a Rapid Optical Lattice Simulator

Project Information

UniRand

Grant agreement ID: 948240

DOI

10.3030/948240

EC signature date 14 August 2020

Start date 1 September 2021

End date 31 August 2026

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 497 701,00

EU contribution

€ 1 497 701,00

Coordinated by

MAX-PLANCK-GESELLSCHAFT ZUR FORDERUNG DER WISSENSCHAFTEN EV
Germany

Periodic Reporting for period 3 - UniRand (Random Unitaries in a Rapid Optical Lattice Simulator)

Reporting period: 2024-09-01 to 2026-02-28

Summary of the context and overall objectives of the project

Understanding quantum many-body systems is one of the hardest open problems in physics: While the ingredients of a particular system can be quite simple to describe (for example a number of interacting particles moving inside a box), the phases and properties that emerge when such systems become larger than a few dozen constituents are extremely hard to predict with classical methods. Fortunately, synthetic quantum systems can come to our help: We can create quantum mechanical systems, whose microscopic ingredients we understand and control, in the lab and simply observe the emerging behavior of many-body physics. Ultracold atoms in optical potentials are a modern experimental system that enables completely new ways of studying the emerging properties of many interacting particles.
Once such a system has been prepared in the lab, a crucial question is how to effectively extract the essential quantum mechanical properties of a many-body system. Technically, ultracold gases under so-called quantum gas microscopes provide the amazing opportunity to image many-particle systems with single-particle resolution. We can take pictures that identify the position and internal state of every particle in the system and that directly show any correlation patterns that may emerge because of their interactions.
There are many open questions on how these technical capabilities can best be used conceptually to understand quantum systems. A very surprising recent theoretical insight is that randomized measurements can provide a lot of insight. While a single measurement of a randomized quantity does not provide any information at all, many such measurements do: Important information, for example about entanglement in a quantum system, is encoded in the fluctuations under random measurements.
The main goal of the project UniRand is to demonstrate the effectiveness of randomized measurements for ultracold atom systems. To this end, we are developing a novel apparatus to prepare ultracold fermionic systems with high repetition rates and to perform proof-of-principle experiments using randomized measurements on phase transitions and non-equilibrium dynamics.
The broader impact of this work is along two main axes: On the one hand, our work is at the forefront of quantum information science. In particular, it provides a bridge between quantum information science (where quantum systems are used for computational tasks) and quantum simulation (where the properties of a particular, classically unsolvable quantum system are explored). Our work will provide a testbed for new theories from the intersection of the two fields. Ultimately, these experiments will provide the scientific community with a better understanding of many-body quantum systems and benefit the public by enabling the design of materials with novel technological properties. On the other hand, we are developing new techniques for the fast preparation, manipulation, and imaging of cold atoms. These can broadly be used in the emerging fields of quantum computation, quantum sensing, and metrology. Over the next decade or so, these techniques are expected to result in enhanced sensors or accelerators for specific computational tasks.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

The first phase of the project has mainly been concerned with the construction of a new apparatus for the production of gases of ultracold lithium in the nanoKelivn regime. To this end, we have developed a new, extremely compact vacuum chamber. Inside the vacuum chamber, atomic lithium vapor is produced by heating liquid lithium to about 350 degrees Celsius. Several stages of laser cooling and evaporative cooling are performed to cool the atoms over many orders of magnitude to sub-microKelvin temperatures and to capture them in optical traps for further manipulation. Over the course of the first 30 months of the project, we have designed, purchased, and assembled all the necessary laser setups, the ultrahigh-vacuum-system, high-current magnetic field coils and control electronics. We have been able to demonstrate laser cooling in a two-dimensional and three-dimensional magneto-optical trap, to count individual atoms in fluorescence, and to load atoms into a deep optical dipole trap. A high-resolution imaging setup has been designed and installed, setting the stage for imaging of atomic samples with single-particle resolution. We have also prepared optical setups for the parallelized trapping of lithium atoms in optical tweezer arrays and to confine them to two-dimensional planes. These milestones demonstrate the core functionality of the machine.
With the technical setup to a large extent done, we are now ready to perform the first key experiments aimed at assembling optical lattice systems from individual atoms and to work towards using randomized measurements on optical lattice systems.
The attached picture gives an impression of the setup of work performed in the lab and the apparatus. We also show a Fermi gas close to degeneracy in an optical dipole trap and the capability to count individual atoms in a microMOT, exemplified by the distinct peaks in a fluorescence count histogram.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

Our progress beyond the state of the art lies in the robust and compact nature of our machine. We opted to use a combination of laser cooling stages that enables a particularly small overall geometry. Our single-chamber design eliminates the need to transport atoms between different parts of the vacuum apparatus. With these choices, the chamber is so small that it can easily fit on translation stages and can be moved between a ‘service position’ and a ‘science position’ on the optical table without effort. This represents a significant simplification: It separates the vacuum chamber and the atomic source from the delicate high-resolution optics surrounding the chamber. Necessary maintenance work on the vacuum chamber can be performed in the ‘service position’ far away from the high-resolution optics, while alignment and calibration tasks of the optics can be performed with the chamber moved out of the way. This makes the overall setup much more predictable and accessible than traditional setups, where a large vacuum chamber often blocks all access to the science cell and renders maintenance operations impossible.
A second success of our work is the use of modular optics. Instead of interleaving beam paths and mounting optical components directly on the optical table, as is customary for most cold atom experiments, we implemented a highly modular approach: Each beam path is set up on a separate breadboard outside the main experiment. The modular breadboards can be placed on a common base plate with high precision using alignment pins. Each module can therefore be pre-aligned and calibrated outside the setup and needs minimal fine alignment once placed in the setup. This hugely simplified procedure greatly reduces the time needed to install new optical traps and allows much more versatile setups. We intend to make this design available publicly and expect that the community will adopt the idea and standards.
Until the end of the project, we expect to proceed along the trajectory towards randomized unitary measurements in optical lattice systems. The next technical goal is to show that lattice systems can be assembled from individual atoms with high ground state fractions. Such assembled lattice systems should reduce the cycle time of cold atom experiments to the one-second timescale and enable the high data rates that are needed to benefit from randomized measurements. We expect to demonstrate the assembly of lattice systems on 5x5 or 10x10 arrays.
Once assembled lattice systems have been demonstrated, we will establish the feasibility of random unitary rotations in optical lattices. To this end, we will install a quasi-periodic superlattice that can implement time-dependent disorder patterns. We will check that dynamics in disordered lattice can produce random unitary rotations with the correct statistics by looking at outcomes of dynamics applied to different programmable initial states.
With these tools in place, we will be in a position to explore the first applications of random unitaries to fermionic Hubbard systems, for example by measuring entanglement entropy in small one- and two-dimensional ground state ensembles.

Impressions of the project work in the lab and first results on trapping cold fermionic gases