^{Physics and Astronomy}

_{Few- and Many-Particle Quantum Systems}

**Example Project: Few- and Many-Particle Quantum Systems**

Faculty Mentor: Qingze Quan

**Dynamics of Ultracold Quantum Gas:**Bose-Einstein condensates (BEC), a phase of condensate matters with a typical temperature close to absolute zero Kelvin, have been realized in experiment [1]. Taking the^{87}Rb as an example, the system is very dilute and behaves like a quantum gas in the ultracold regime. The low-energy feature of the system makes it well under control and precisely engineered for quantum simulations. Synthetic gauge fields, synthetic dimensions, and optical lattice potentials in ultracold atomic systems are all active research topics today [2, 3]. The system usually contains millions of particles which makes it impossible to solve without any approximation. The REU students who are interested in the topic will be trained to gain the concepts of many-body physics, quantum simulations, the mean-field approximation, and the beyond mean-field physics. Both analytical and numerical skills will be developed through doing this research.**Quantum Dynamics of Few Particles:**With the development of the optical tweezer technique, the laser cooling technique, and the single-particle imaging technique, clean quantum systems consisting of a few particles have been created in experiment with high fidelity nowadays [4]. The high tunability of the few-particle system makes them ideal platforms to perform various types of quantum technologies,*e.g.,*quantum sensing, quantum computing, and quantum chemistry. By adding particles one by one, the few-body system provides a “bottom-up” tool to understand the many-particle physics such as thermalization in closed quantum systems, dynamics in strongly correlated systems, universal properties in many-body systems, and quantum chaos [5, 6]. The REU students who are interested in the research topic will be exposed the opportunity of solving one-, two- and three-particle Schrodinger equations analytically and numerically. The numerical calculations will involve developing your own code from scratch possibly with the parallel computing algorithm. The concept of quantum scattering, universalities, and quantum correlations will be widely discussed.**Quantum Sensing and Quantum Metrology:**Precisely measuring a physical quantity plays a crucial role in advancing the modern physics. Examples cover measuring the gravitational waves to validate the Einstein’s general relativity and measuring the Higgs Bosons to validate the mass generation mechanism of the Standard Model. Taking advantage of entanglements, a quantum sensor with an accuracy that beats the limit of a corresponding classical system can be established [7]. Such a tensor can be a many-particle system near a critical point, an interferometer based on atomic and optical systems, a superconducting qubit,*et al*[8, 9]. Designing a proper protocol of generating useful entanglement, benchmarking the best performance, and testing the stability of the quantum sensor are the key aspects of this topic. The REU students will learn the concepts of useful entanglements, quantum Fisher information, Heisenberg limit, and quantum interferometers through doing this research. Analytical works based on toy model studies and numerical calculation such as diagonalizing the Hamiltonian matrix and time evolving the density matrices will be used here.

**Undergraduate Research:** Dr. Qingze Guan, as a new P.I. starting from Fall 2022, is currently building up his own research group. Currently, he is advising two graduate students and one undergraduate student on their quantum theory projects. You are welcome to join the group where you will solve cool quantum problems and talk to people who love quantum mechanics.

[1] F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” *Rev. Mod. Phys.* **71**, 463 (1999).

[2] Q. Guan, T. M. Bersano, S. Mossman, P. Engels, and D. Blume, “Rabi oscillations and Ramsey-type pulses in ultracold bosons: Role of interactions,” *Phys. Rev. A* **101**, 063620 (2020).

[3] Q. Guan, M. K. H. Ome, T. M. Bersano, S. Mossman, P. Engels, and D. Blume, “Nonexponential Tunneling due to Mean-Field-Induced Swallowtails,” *Phys. Rev. Lett*. **125**, 213401 (2020).

[4] F. Serwane, G. Zürn, T. Lompe, T. B. Ottenstein, A. N. Wenz, and S. Jochim, “Deterministic Preparation of a Tunable Few-Fermion System,” *Science* **332**, 336 (2011).

[5] Q. Guan, V. Klinkhamer, R. Klemt, J. H. Becher, A. Bergschneider, P. M. Preiss, S. Jochim, and D. Blume, “Density Oscillations Induced by Individual Ultracold Two-Body Collisions,” *Phys. Rev. Lett.* **122**, 083401 (2019).

[6] M. Kunitski, Q. Guan, H. Maschkiwitz, J. Hahnenbruch, S. Eckart, S. Zeller, A. Kalinin, M. Schöffler, L. Ph. H. Schmidt, T. Jahnke, D. Blume, and R. Dörner, “Ultrafast manipulation of the weakly bound helium dimer,” *Nature Physics* **17**, 174 (2020).

[7] L. Pezzè, A. Smerzi, M. K. Oberthaler, R. Schmied, and P. Treutlein, “Quantum metrology with nonclassical states of atomic ensembles,” *Rev. Mod. Phys.* **90**, 035005 (2018).

[8] Q. Guan, G. W. Biedermann, A. Schwettmann, and R. J. Lewis-Swan, “Tailored generation of quantum states in an entangled spinor interferometer to overcome detection noise,” *Phys. Rev. A* **104**, 042415 (2021).

[9] Q. Guan and R. J. Lewis-Swan, “Identifying and harnessing dynamical phase transitions for quantum-enhanced sensing,” *Phys. Rev. Research* **3**, 033199 (2021).