LABORATOIRE DE PHYSIQUE ET MODELISATION DES MILIEUX CONDENSES

Superconducting circuits (SCs) are quantum devices that mimic the behavior of atomic systems even though they are made up of macroscopic microwave circuit elements. Their tunability, high coherence, and strong coupling has led to their rapid development as a leading implementation of quantum hardware. Traditional SCs are made using known superconductors such as aluminum or niobium, but the integration of novel superconductors as part of the circuit can lead to new scientific insights and new capabilities. Such hybrid circuits are ideal sensors, capable of measuring the superconducting gap structures of novel materials using micron-sized samples, which is especially useful for interface superconductors or van-der-Waals flakes which cannot be probed with bulk techniques. Furthermore, the unique quantum properties of unconventional superconductors can be utilized to make a new class of quantum devices. This talk will present recent results where we explore van-der-Waals superconductors in cuprate and kagome systems with hybrid circuits, and a path towards utilizing them in new hybrid devices for quantum technology.

Most quantum technologies and protocols rely on the use of pure quantum states. One approach to increase the purity of a quantum state is to apply purification protocols, which aim to reduce the entropy of an initially mixed state. Generally these protocols rely on measurements and feedback in order to reduce entropy. Even though multiple protocols [1–4] and bounds [5, 6] have been proposed for quantum state purification, the fundamental mechanisms underlying these processes have yet to be uncovered. In this work, we identify two fundamental mechanisms underlying a purification process. The first, that we dub classical purification, alters the probability distribution of the mixed state in order to reduce its entropy [2, 3]. A prime example of a process solely using classical purification is the Maxwell’s demon experiment [7], where the demon sorts out high energy gas particles from lower energy ones, thereby reducing the entropy of the gas. The second, that we dub quantum purification, generates quantum indistinguishability between the quantum states which make up the mixture. This is as if the demon was to superpose the gas particles making them partially indistinguishable rather than sorting them. This process decreases the entropy of the gas solely using quantum purification. Concretely, we consider the purification of optical systems via a qubit (counterpart of the demon) where we illustrate our ideas on experimentally viable processes such as the preparation of Schr¨odinger cats, where both quantum and classical purification can be observed and SNAP [8] operations where solely quantum purification can be observed. Finally, we provide a pathway towards quantum cooling processes where both the entropy and energy of a state is lowered by generation of quantum indistinguishability.

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[2] C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, Purification of noisy entanglement and faithful teleportation via noisy channels, Phys. Rev. Lett. 76, 722 (1996).

[3] A. M. Alhambra, M. Lostaglio, and C. Perry, Heat-bath algorithmic cooling with optimal thermalization strategies, Quantum 3, 188 (2019).

[4] A. V. Lebedev, D. Oehri, G. B. Lesovik, and G. Blatter, Trading coherence and entropy by a quantum maxwell demon, Phys. Rev. A 94, 052133 (2016).

[5] M. A. Nielsen, Characterizing mixing and measurement in quantum mechanics, Phys. Rev. A 63, 022114 (2001).

[6] K. Jacobs, Efficient measurements, purification, and bounds on the mutual information, Phys. Rev. A 68, 054302 (2003).

[7] J. C. Maxwell, Theory of Heat, Cambridge Library Collection - Physical Sciences (Cambridge University Press, 2011).

[8] R. W. Heeres, B. Vlastakis, E. Holland, S. Krastanov, V. V. Albert, L. Frunzio, L. Jiang, and R. J. Schoelkopf, Cavity state manipulation using photon-number selective phase gates, Phys. Rev. Lett. 115, 137002 (2015).

The helical edge of a quantum spin Hall insulator hosts a one-dimensional metallic state with spin-momentum locking, realizing a helical Luttinger liquid (HLL). While the gapless phase is well understood analytically through bosonization in its simplest form, more complex questions that demand numerical treatment, have remained largely inaccessible to address for a long time. The core obstacle is the fermion-doubling problem: any local and symmetry-preserving discretization of the Hamiltonian on a strictly one-dimensional lattice either introduces spurious low-energy modes or lifts the Dirac point, breaking the topological protection of the cone.
In this talk I describe how this obstruction can be circumvented using a tangent fermion discretization. This preserves time-reversal symmetry and spin-momentum locking at the lattice level, without invoking a two-dimensional bulk. I present the application of this method first to the gapless HLL, where numerical results are in quantitative agreement with bosonization predictions, establishing the framework as a reliable numerical tool. And then I turn to interaction-induced mass generation, including spontaneous time-reversal symmetry breaking in HLL and symmetric mass generation in 3-4-5-0 model, where full analytical treatment is out of reach.