Szymon Pustelny

SZYMON PUSTELNY

Scientist, entrepreneur, husband, and father

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QUANTUM-STATE ENGINEERING
AND
QUANTUM-STATE TOMOGRAPHY

The manipulation and control of quantum states holds the key to realizing the full potential of quantum mechanics in various practical applications. Our research focuses on utilizing room-temperature atomic vapor and the interplay of light and magnetic fields to establish a robust and reliable platform for the controllable generation and detection of complex collective quantum states in atomic vapor.

INTRODUCTION

Quantum mechanics presents numerous opportunities for technological advancement, particularly in the realm of secure cryptography and problem-solving. To realize these possibilities, it is necessary to establish a comprehensive methods for the controllable manipulation and detection of quantum states. The challenge of manipulating quantum states arises from the phenomenon of decoherence, which manifests as a degradation of quantum properties of objects. Moreover, ever-preset noise leads to uncertainty in the determination and manipulation of quantum states, hindering the development of reliable applications.This presents particular difficulties in conventional implementations of qubits, such as single atoms/ions, photons, or superconducting circuits, where measured signals are weak.

COLLECTIVE QUANTUM STATE

Alternatively to the operation with quantum states of single objects, one can consider utilization of collective quantum states of ensembles of quantum particles. The states encompass the quantum properties of each particle in the ensemble, providing a representation of the system as a whole. While collective quantum states can exhibit distinct behavior from that of individual particles, it can still remain (some) quantum properties and can be used both for research and practical applications.

 

From the practicalstandpoint, incorporation of a greater number of particles with the same quantum state results in enhanced experimental signals, but also enables the implementation of the so-called quantum nondemolition measurements that have a limited impact on the quantum state of the system under observation.

ROOM-TEMPERATURE ATOMIC VAPOR

A convenient platform for the implementation of reserach using collective quantum state are room-temperature alkali-metal vapors, such as those of rubidium or cesium, interacting with external field (light and static and oscillating magnetic field). This implementation offers several advantages, including the ability to generate complex, yet long-lived quantum states, as well as the ability to perform nondestructive retrievals of the information. The former offers the ability to tailor complex quantum state, while the latter enables a complete tomography of the system, which can be used to test quantum properties of the system. A particular advantage of operation with such systems is that experimental setups enabling generation, manipulation, and detection of the signals can be relatively simple and even miniaturized, which could have important implications for practical applications.

QUANTUM REGISTERS

In the realm of quantum computation, it is necessary to aggregate qubits into larger structures known as quantum registers. For computing, qubits in the register need to be precisely controlled and the ability of generating superpositions of multiple qubits needs to be provided. A common method to achieve this goal is through the construction of strongly interacting microscopic systems (chain of ions, neutral atoms in optical lattice, etc.), where the state of one qubit affects the state of a specific other qubit within the register. However, the strong interaction between the qubits also leads to strong coupling of the qubits with environment. This results in decoherence and reduction of lifetime of the register as the number of qubits increases.
Complex qudit visualized

QUDITS

As an alternative, qudits, multi-state systems, which can hold more information than binary qubits, can be used. The ability to use systems with a larger number of energy levels allows for the creation of more complex quantum states, including those with multiple-level quantum superpositions. With more dimensions, the qudit offers the potential for implementing more complex quantum algorithms, though their manipulation and control can present a greater challenge as compared to qubits. An additional advantage of this approach lies in the absence of strong environmental interactions that cause decoherence. This leads to longer lifetimes for qudits, which is crucial for various applications.

PHYSICAL IMPLEMENTATION OF QUDITS

As discussed above, the utilization of hyperfine ground states of alkali-metal atoms is a promising approach for the implementation of qudits. Due to the uncoupled electron at the valence shell, the alkali-metal atoms have two hyperfine levels, which, depending on the element/isotope, have from three to nine magnetic sublevels that can be used for decoding quantum information. In specially prepared containers, the lifetime of a complex state of the levels can exceed 100 ms. The advantage of alkali-metal elements also lies in their excitation/addressability with braodly available semiconductor lasers (near infrared range). Thereby, through optical pumping with appropriately polarized light and application of static and oscillating magnetic fields the complex quantum states can be generated, which is main motivation for our research.
Qudit setup

HIGHER-ORDER COHERENCES

One of the distinctive features of our research is the ability to generate higher-order coherences, i.e., the superpositions of states differing in a magnetic quantum number by more than two, within a given hyperfine level. While in conventional approaches, one can only controllably produce superpositions betweem sublevels of magnetic number less than or equal to two, we go beyond this limitation by utilizing nonlinear light-atom interaction. To ensure the ability of generating of specific coherences, we additionally exploit the symmetries of the electronic cloud associated with each of the coherences. For instance, the state with a coherence difference of two is characterized by a two-fold symmetry, while the superpositions with magnetic quantum-number differences equal to four and six are associated with electronic distributions exhibiting four- and six-fold symmetries, respectively. To take advantage of these symmetries, we employ nonlinear magneto-optical rotation in conjunction with stroboscopic optical pumping. This approach involves modulation of linearly polarized light at a specific multiple of the Larmor frequency, which results in the selective generation of given coherences.

TRANSFERING WHOLE QUANTUM STATE

The existence of two long-lived hyperfine ground states within alkali atomic vapor rises a question of the ability to the transfer of a complete quantum state between two physical energy levels. While the transfer of populations between states is well-established in atomic physics and is known as STIRAP, we investigate the transfer of populations of magnetic sublevels between hyperfine states. Our research has shown that not only is this transfer possible, but the transfer can be selectively controlled through the proper tuning of the light beams used without the need for additional measures like application of strong magnetic fields. This simplifies the experimental implementation of the approach. Our future research aims at transferring the complete quantum state between the hyperfine states. Theoretical analysis shows that by carefully selecting the parameters of the light beams, the entire state, including both sublevels’ populations and superpositions, can be transferred. If successful, this experimental implementation could open up the possibility of implementing a quantum processor – quantum memory system.
Quantum-state reconstruction

QUANTUM-STATE TOMOGRAPHY

The critical aspect of quantum information science is the ability to accurately reconstruct a quantum state. State tomography not only enables retrieval of information stored within a system, but also serves as a means of evaluating information manipulation protocols.

 

In our study, which utilizes a room-temperature rubidium vapor, full state tomography is achieved through quantum non-demolition measurements using light. By measuring the polarization of light traversing through the medium whose collective quantum state is being determined, we are able to reconstruct the quantum state of the medium. Unlike other approaches, our method takes into account the full light-atom interaction, including the tensorial contribution to the light-atom interaction. This approach allowed us to reconstruct the quantum state of the hyperfine level of total angular momentum equal to unity. As shown with our theoretical analysis, the technique is highly robust against noise and experimental uncertainties, leading to very high fidelity reconstructions. This represents a significant step forward in our ability to extract and utilize quantum information for a wide range of applications, making this a truly exciting and cutting-edge area of research.

TEST OF QUANTUMNESS

Our research also focuses on testing atomic-vapor contextuality. In quantum mechanics, contextuality refers to the idea that the outcome of a quantum measurement depends not only on the system being observed, but also on the set of observables that are being measured simultaneously. We test the property by examining the correlations between particle spins within a room-temperature atomic vapor.

 

We are also testing genealized Bell inequalities for qudits, which provide evidence of non-locality. From the theoretical standpoint, qudits are expected to be more resilient to noise compared to other systems. However, such claims are typically based on a specific noise model. With our research we test the inequalities under a more realistic conditions. The high accuracy of the quantum state reconstructions allows us to analyze this key quantum property of physical systems.

Contextuality

Selected publications

Scientific articles:.

  • M. Kopciuch and S. Pustelny, Optical reconstruction of the collective density matrix of a qutrit, Physical Review A 106, 022406 (2022) – Preprint.

  • A. Sierant, M. Kopciuch, and S. Pustelny, Tailoring population transfer between two hyperfine ground states of Rb87 – Preprint

  • §  S. Pustelny, M. Koczwara, L. Cincio, and W. Gawlik, Tailoring quantum superpositions with linearly polarized amplitude-modulated light, Physical Review A 83, 043832 (2011) – Full version.