Quantum Trajectories

We have tried to describe how the interplay between the system environment coupling and external driving frequency shapes the dynamical properties and steady state behavior in a periodically driven transverse field Ising chain subject to measurement. We have analyzed the fate of the steady state entanglement scaling properties as a result of a measurement induced phase transition. We have explained how such steady state entanglement scaling can be computed analytically using asymptotic features of the determinant of associated correlation matrix which turned out to be of block Toeplitz form. We have pointed out the differences from the Hermitian systems in understanding the entanglement scaling behav-ior in regimes where the asymptotic analysis can be performed using Fisher-Hartwig con-jecture. Finally we have discussed how the tuning of the drive frequency controls the do- main of applicability of the Fisher-Hartwig conjecture and the emergence of the long range ordering of the effective Floquet Hamiltonian governing the properties of the system.

What happens when the unitary evolution of a generic closed quantum system is interrupted at random times with non-unitary evolution due to interactions with either the external environment or a measuring apparatus? We adduce a general framework to obtain the average density operator of a generic quantum system experiencing any form of non-unitary interaction. We provide two explicit applications in the context of the tight-binding model for two representative forms of interactions: (i) stochastic resets and (ii) projective measurements at random times. For the resetting case, our exact results show how the particle is localized on the sites at long times, leading to a time-independent mean-squared displacement. For the projective measurement case, repeated projection to the initial state results in an effective suppression of the temporal decay in the probability of the particle being in the initial state. The amount of suppression is comparable to the one in conventional Zeno effect scenarios, where measurements are performed at regular intervals.

Purification is a notable property of quantum trajectories. As time grows, mixed states tend to converge towards pure states. In 2005 Kümmerer and Maassen provided necessary and sufficient conditions for a full purification of quantum trajectories. In 2019, with some collaborators, we used purification to show that, under the assumptions of Kümmerer and Maassen, we can classify the full set of stationary distributions for quantum trajectories.

In this presentation, after reviewing these results, I will focus on what happens when the conditions of Kümmerer and Maassen are not fulfilled. Then, some dark subspaces appear. I will explain how we were able, with Anna Szczepanek and Clément Pellegrini, still, to classify all the stationary distributions of quantum trajectories. Since dark subspaces are also relevant to quantum error correction, I will try to put some bridges with our results. I will also mention ideas related to the same work but for imperfect measurements.

This presentation concerns the preprint arXiv:2409.18655.

Quantum thermodynamics is an active research area bridging quantum information and nonequilibrium statistical physics. A key to characterize universal behaviors of entropy production is the fluctuation theorem, which leads to the second law of thermodynamics in the regime far from equilibrium. The fluctuation theorem in classical systems has been thoroughly studied under various feedback control setups by incorporating classical information contents, which sheds modern light on "Maxwell's demon" [1]. However, an intriguing situation in quantum systems, such as continuous (or iterative) measurement and feedback, remains to be investigated.

In this talk, I will first present our theoretical results on the generalized fluctuation theorem and the second law under continuous measurement and feedback [2]. The key ingredient is a newly introduced concept to measure quantum information flow, which we call quantum-classical-transfer (QC-transfer) entropy. QC-transfer entropy can be naturally interpreted as the quantum counterpart of transfer entropy that is commonly used in classical time series analysis.

I will then present our recent collaborating work on an experiment [3]. We employ a state stabilization protocol involving repeated measurement and feedback on an electronic spin qubit associated with a Silicon-Vacancy center in diamond, which is strongly coupled to a diamond nanocavity. This setup allows us to verify the fundamental laws of nonequilibrium quantum thermodynamics, including the second law and the fluctuation theorem, both of which incorporate QC-transfer entropy mentioned above. We further assess the reducible entropy based on the feedback's causal structure and quantitatively demonstrate the thermodynamic advantages of non-Markovian feedback over Markovian feedback. These results reveal a fundamental connection between information and thermodynamics in the quantum regime.

[1] J. M. Parrondo, J. M. Horowitz, and T. Sagawa, Nature Physics 11, 131 (2015).
[2] T. Yada, N. Yoshioka, and T. Sagawa, Phys. Rev. Lett. 128, 170601 (2022).
[3] T. Yada*, P-J. Stas*, A. Suleymanzade, E. Knall, N. Yoshioka, T. Sagawa, and M. Lukin, arXiv:2411.06709 (2024). *: co-first authors

SME of  the photon box: wave-function/density-operator  formulation, dispersive/resonant  propagator, Markov model, quantum Monte-Carlo trajectories, (super)-matringales, Quantum Non Demolition (QND) measurement of photons, Bayesian inference to include measurement imperfections and decoherence,   simulation and convergence analysis.

It is now common to say that photons can be transmitted along optical fibers or transmission lines. But in many cases, the transmission pulse is defined by a time profile of the field strength, i.e., the electric field or voltage V(t), at the transmission point. How does this turn into a precise description of the arrival profile of the photons in the pulse? We show that there is a highly nontrivial mathematical relation between the function V(t) and the arrival function of the photons. Paradoxically, when V(t) is strictly limited in time, the photon arrival profile cannot be. This, and the counterintuitive relation between V(t) and the expected number of arriving photons, has consequences for the security of quantum cryptography.

PNAS 121 (4) e2314846121 (2024).

The quantization of gravity is widely believed to result in gravitons -- particles of discrete energy that populate gravitational waves. But their detection has so far been considered impossible. In this talk, I will first show that signatures of single graviton exchanges between matter and gravitational waves can be observed in laboratory experiments. Stimulated and spontaneous single-graviton processes can become relevant for massive quantum acoustic bar resonators, where the stimulated absorption of single gravitons can be resolved through continuous sensing of quantum jumps. In analogy to the discovery of the photo-electric effect for photons, such signatures can provide the first experimental clue of the quantization of gravity.
I will conclude the talk by showing that further statistical tests that probe the quantum mechanical character of radiation fields are also possible, using the counting statistics of observed quantum jumps in resonant detectors. I will present simple statistical tests which provide practical means to test the null hypothesis that a given field is "maximally classical", i.e., accurately described by a coherent state. Our findings suggest circumstances in which that hypothesis plausibly fails, notably including gravitational radiation involving non-linear or stochastic sourcing.

References:
[1] Germain Tobar*, Sreenath K. Manikandan*, Thomas Beitel, and Igor Pikovski. "Detecting single gravitons with quantum sensing."Nature Communications 15, 7229 (2024)

[2] Sreenath K. Manikandan and Frank Wilczek, Detecting Acoherence in Radiation Fields, ArXiv 2409.20378 (2024)