PUSTELNY GROUP
Quantum Sensing, Fundamental Physics, Spin Systems
QUANTUM-STATE ENGINEERING
AND QUANTUM TOMOGRAPHY
Using room-temperature alkali-metal vapors in anti-relaxation-coated cells, we prepare and coherently control collective multilevel spin states (qudits). Through optical quantum-state and process tomography, we reconstruct both their quantum states and the dynamics governing their evolution, connecting quantum-state engineering, precision measurement, and foundational studies of quantum mechanics.
COLLECTIVE SPIN ENSEMBLES
Alongside experiments on single trapped ions, neutral-atom arrays, or superconducting circuits, quantum-state preparation and readout can be implemented in macroscopic ensembles of 1010–1012 identical atoms. Collective spin ensembles retain single-atom internal Hilbert-space structure while providing high optical signal-to-noise ratios in weak, minimally perturbative dispersive polarimetry.
WARM ATOMIC-VAPOR PLATFORM
Our experiments use room-temperature rubidium and cesium vapors confined in evacuated glass cells with anti-relaxation wall coatings and surrounded by multi-layer magnetic shielding. These coatings strongly reduce spin depolarization during wall collisions, allowing long-lived ground-state spin coherence without laser cooling or ultra-high vacuum.
This combination of long coherence times, optical accessibility, and experimental simplicity makes warm atomic vapors an attractive platform for quantum control and state reconstruction in multilevel spin systems.
MULTILEVEL QUANTUM SYSTEMS (QUDITS)
Unlike a qubit, which stores quantum information in two levels, a qudit occupies a Hilbert space of dimension (d > 2). In alkali-metal atoms, the hyperfine and Zeeman structure of the ground state naturally provides access to such multilevel systems.
These high-dimensional states allow compact encoding of angular-momentum structure and support sensing and control protocols that have no direct two-level analogue. At the same time, they require coherent manipulation of multiple coupled spin coherences, making them a rich setting for both quantum metrology and quantum-state engineering.
HYPERFINE ENCODING & ZEEMAN CONTROL
A central part of our research is the coherent control of spin states within and between hyperfine manifolds. In warm alkali vapors, this requires resolving and manipulating transitions that may become difficult to distinguish at low magnetic fields.
We investigate optical and magnetic control methods that enable selective access to multilevel spin dynamics, including synchronous optical pumping, control of quadratic Zeeman structure, and the generation of higher-order polarization moments. These higher-order coherences encode nontrivial rotational symmetries of the collective spin state and extend the range of quantum states that can be prepared and studied experimentally.
COHERENT TRANSFER BETWEEN HYPERFINE MANIFOLDS
Full control of alkali-metal qudits requires more than addressing individual Zeeman coherences within a single manifold. It also requires coherent transfer between hyperfine manifolds, enabling access to the full multilevel ground-state space.
Our work explores Raman- and STIRAP-like optical control schemes for transferring populations and coherences in room-temperature ensembles while minimizing decoherence. These approaches extend the toolbox of state engineering beyond simple optical pumping and open routes to more versatile multilevel control.
OPTICAL QUANTUM-STATE TOMOGRAPHY
Preparing complex qudit states is only useful if they can be reliably characterized. We therefore develop continuous, non-destructive optical quantum-state tomography based on off-resonant polarimetric detection.
By combining controlled spin evolution with optical readout sensitive to both vector and tensor atomic polarizability, we reconstruct the collective density matrix and access populations as well as higher-order coherences. This approach allows quantum-state reconstruction in warm atomic vapors without destroying the ensemble and provides a direct way to validate state preparation and coherent control protocols.
Verifying arbitrary qudit operations requires reconstructing the complete collective density matrix ρ. We developed continuous, non-destructive optical state tomography based on off-resonant polarimetric readout—exploiting both vector (paramagnetic Faraday rotation) and tensor (linear birefringence / Voigt) atomic polarizability components—while evolving the spins under controlled magnetic-field rotations. Demonstrated first on an F = 1 qutrit (Physical Review A 2022) and subsequently optimized across higher-dimensional alkali ground manifolds (Physical Review A 2024), this protocol reconstructs populations and arbitrary-order coherences in a single experimental trajectory.
QUANTUM PROCESS TOMOGRAPHY & OPEN-SYSTEM DYNAMICS
While quantum-state tomography reveals the state of a quantum system, quantum process tomography (QPT) allows us to investigate how that state evolves under coherent control and environmental interactions. Using room-temperature ⁸⁷Rb atomic ensembles, we reconstruct the dynamics of collective qutrit states by preparing different initial states and monitoring their evolution through optical measurements.
Our research extends this approach to Liouvillian tomography, enabling the reconstruction of both coherent and dissipative contributions to quantum evolution. By characterizing relaxation, magnetic-field perturbations, and time-dependent spin control, we gain insight into the mechanisms that govern the performance of realistic quantum systems. These methods provide new opportunities for noise characterization, quantum-control benchmarking, and precision sensing.
QUANTUM METROLOGY & QUANTUM FOUNDATIONS
High-dimensional collective spin states are interesting not only as a control problem, but also because they enable new applications in precision measurement and foundational studies of quantum mechanics.
Together with theoretical collaborators, we investigate quantum states optimized for directional and rotational sensing, including so-called quantum protractors, and we explore how full multilevel control can be used to test single-qudit quantum contextuality under realistic experimental conditions. These directions connect atomic-spin physics with broader questions about the structure, limits, and interpretation of quantum theory.
SELECTED PUBLICATIONS IN QUANTUM-STATE ENGINEERING
- [Physical Review Applied 2025] A. Fard, M. Kopciuch, Y. Sun, P. Włodarczyk, and S. Pustelny, Isolating pure quadratic Zeeman splitting, Physical Review Applied 23, 064034 (2025) — DOI
- [Quantum 2024] M. Piotrak, M. Kopciuch, A. D. Fard, M. Smolis, S. Pustelny, K. Korzekwa, Perfect quantum protractor, Quantum 8, 1459 (2024) — DOI
- [Scientific Reports 2024] P. Gladysz, S. Pustelny, and K. Slowik, Superluminal light propagation in a three-level ladder system, Scientific Reports 14, 15151 (2024) — DOI
- [Physical Review A 2024] M. Kopciuch, M. Smolis, A. Miranowicz, and S. Pustelny, Optimized optical tomography of quantum states of a room-temperature alkali-metal vapor, Physical Review A 109, 032402 (2024) — DOI
- [Physical Review A 2023] A. Sierant, M. Kopciuch, and S. Pustelny, Tailoring population transfer between two hyperfine ground states of 87Rb, Physical Review A 107, 052810 (2023) — DOI
- [Physical Review A 2022] M. Kopciuch and S. Pustelny, Optical reconstruction of the collective density matrix of a qutrit, Physical Review A 106, 022406 (2022) — DOI
- [Physical Review A 2011] S. Pustelny, M. Koczwara, L. Cincio, and W. Gawlik, Tailoring quantum superpositions with linearly polarized amplitude-modulated light, Physical Review A 83, 043832 (2011) — DOI
- [Proceedings of SPIE 2011] G. P. Djotyan, N. Sandor, J. S. Bakos, Zs. Bakos, W. Gawlik, A. Wojciechowski, J. Zachorowski, S. Pustelny, and G. Yu. Kryuchkyan, Creation and measurement of coherent superposition states in multilevel atoms, Proceedings of SPIE 7998, 79981A (2011)
- [Physical Review A 2009] R. Drampyan, S. Pustelny, and W. Gawlik, Electromagnetically induced transparency versus nonlinear Faraday effect: Coherent control of light-beam polarization, Physical Review A 80, 033815 (2009) — DOI
- [Optics Express 2008] V. M. Acosta et al., Production and detection of atomic hexadecapole at Earth's magnetic field, Optics Express 16, 11423 (2008)