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Physical Review A

Experimental realization of quantum state engineering with single photons

Xiaojian Huang, Lei Xiao, Kunkun Wang, Peng Xue

Published Nov 26, 2024• 1 citation
Publisher

Abstract

Fully controlling the transformation of an arbitrary quantum state to a predesigned state is a crucial technology in quantum information processing. Despite numerous efforts in pursuit of this objective, a truly viable method remains elusive. Here we successfully devise an experiment capable of engineering any state on the Bloch sphere to a predetermined target state. To validate our findings, we choose different initial states to evolve and compare the purity and fidelity of the evolved state with the target state. Furthermore, we investigate the relationship between the steering speed and the spectrum of the Liouvillian superoperator, proposing an approach to speed up the steering process. Notably, we observe that setting system parameters at the Liouvillian exceptional point (LEP) leads to the fastest evolution to the steady state. In cases without an LEP, a larger Liouvillian gap corresponds to quicker convergence to the steady state. Our method introduces a different avenue for studying Liouvillian dynamics in open quantum systems and provides a practical means for state manipulation.

DOI
10.1103/physreva.110.053717

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Fully controlling the transformation of an arbitrary quantum state to a predesigned state is a crucial technology in quantum information processing. Despite numerous efforts in pursuit of this objective, a truly viable method remains elusive. Here we successfully devise an experiment capable of engineering any state on the Bloch sphere to a predetermined target state. To validate our findings, we choose different initial states to evolve and compare the purity and fidelity of the evolved state with the target state. Furthermore, we investigate the relationship between the steering speed and the spectrum of the Liouvillian superoperator, proposing an approach to speed up the steering process. Notably, we observe that setting system parameters at the Liouvillian exceptional point (LEP) leads to the fastest evolution to the steady state. In cases without an LEP, a larger Liouvillian gap corresponds to quicker convergence to the steady state. Our method introduces a different avenue for studying Liouvillian dynamics in open quantum systems and provides a practical means for state manipulation.
The state of a quantum system may be steered towards a predesignated target state, employing a sequence of weak blind measurements (where the detector's readouts are traced out). Here we analyze the steering of a two-level system using the interplay of a system Hamiltonian and weak measurements and show that any pure or mixed state can be targeted. We show that the optimization of such a steering protocol is underlain by the presence of Liouvillian exceptional points. More specifically, for high-purity target states, optimal steering implies purely relaxational dynamics marked by a second-order exceptional point, whereas for low-purity target states, it implies an oscillatory approach to the target state. The dynamical phase transition between these two regimes is characterized by a third-order exceptional point.
The state of a quantum system may be steered towards a predesignated target state, employing a sequence of weak blind\textit{blind}blind measurements (where the detector's readouts are traced out). Here we analyze the steering of a two-level system using the interplay of a system Hamiltonian and weak measurements, and show that any\textit{any}any pure or mixed state can be targeted. We show that the optimization of such a steering protocol is underlain by the presence of Liouvillian exceptional points. More specifically, for high purity target states, optimal steering implies purely relaxational dynamics marked by a second-order exceptional point, while for low purity target states, it implies an oscillatory approach to the target state. The phase transition between these two regimes is characterized by a third-order exceptional point.
Pure-state inverse engineering among the schemes of shortcuts to adiabaticity is a widespread utility in applications to quantum computation and quantum simulation. While in principle it can realise the fast control of quantum systems with high fidelity, in practice this fast control is severely hindered by infinite energy gaps and impractical control fields. To circumvent this problem, we propose a scheme of shortcuts to adiabaticity of mixed state based on the dynamical invariant of open quantum system. Our scheme can drives a steady state to a target steady state of the open system by a controlled Liouvillian that possesses the same form as the reference (original) one. We apply this scheme to stimulated Raman adiabatic passage (STIRAP) and find that an almost perfect population transfer can be obtained. The experimental observation with currently available parameters for the nitrogen-vacancy (NV) center in diamond is suggested and discussed.
One of the most remarkable features that distinguish open systems from closed ones is the presence of exceptional points (EPs), where two or more eigenvectors of a non-Hermitian operator coalesce, accompanying the convergence of the corresponding eigenvalues. So far, EPs have been demonstrated on a number of platforms, ranging from classical optical systems to fully quantum-mechanical spin-boson models. In these demonstrations, the reservoir that induced the non-Hermiticity was treated as a Markovian one, without considering its memory effect. We here present the first experimental demonstration of non-Markovian quantum EPs, engineered by coupling a Josephson-junction-based qubit to a leaky electromagnetic resonator, which acts as a non-Markovian reservoir. We map out the spectrum of the extended Liouvillian superoperator by observing the quantum state evolution of the qubit and the pseudomode, in which the memory of the reservoir is encoded. We identify a twofold second-order EP and a third-order EP in the Liouvillian spectrum, which cannot be realized with a Markovian reservoir. Our results pave the way for experimental exploration of exotic phenomena associated with non-Markovian quantum EPs.
We investigate speeding up of relaxation of Markovian open quantum systems with the Liouvillian exceptional point (LEP), where the slowest decay mode degenerates with a faster decay mode. The degeneracy significantly increases the gap of the Liouvillian operator, which determines the time scale of such systems in converging to stationarity and thus accelerates the relaxation process. We explore an experimentally relevant three-level atomic system whose eigenmatrices and eigenspectra are obtained completely analytically. This allows us to gain insights into the LEP and examine the respective dynamics with details. We illustrate that the gap can be further widened by Floquet engineering, which further accelerates the relaxation process. Finally, we extend this approach to analyze laser cooling of trapped ions, where vibrations (phonons) couple to the electronic states. An optimal cooling condition is obtained analytically, which agrees with both existing experiments and numerical simulations. In this paper, we provide analytical insights into understanding LEP as well as controlling and optimizing the dissipative dynamics of atoms and trapped ions.
We propose a fast mixed-state control scheme to transfer the quantum state along designable trajectories in Hilbert space, which is robust to multiple decoherence noises. Starting with the dynamical invariants of open quantum systems, we present the shortcuts to adiabaticity (STA) of open quantum systems at first, then apply the STA to speed up the adiabatic steady process. Our scheme drives open systems from a initial steady state to a target steady state by a controlled Liouvillian that possesses the same form as the reference (original) one that is accessible in present-day experiments. An experimental design with currently available parameters for the nitrogen-vacancy (N-VVV) center in diamond is suggested and discussed.