Exceptional points (EPs) are ubiquitous in non-hermitian systems, and represent the complex counterpart of  critical points. By driving a system through a critical point at finite rate induces defects, described by the Kibble-Zurek mechanism, which finds applications in diverse fields of physics. Here we generalize this to a ramp across an EP. We find that  adiabatic time evolution brings the system into an eigenstate of the final non-hermitian Hamiltonian and demonstrate that for a variety of drives through an EP, the defect density obeys a universal scaling form in terms of the usual critical exponents and the speed of the drive. Defect production is suppressed compared to the conventional hermitian case as the defect state can decay back to the ground state close to the EP.

Title: "Superfluid weight and polarization amplitude in the one-dimensional bosonic Hubbard model"

Abstract: "We calculate the superfluid weight and the polarization amplitude for the one-dimensional bosonic Hubbard model focusing on the strong-coupling regime. Other than analytic calculations we apply two methods: variational Monte Carlo based on the Baeriswyl wave function and exact diagonalization. The former gives zero superfluid response at integer filling, while the latter gives a superfluid response at finite hopping. From the polarization amplitude we derive the variance and the associated size scaling exponent. Again, the variational study does not produce a finite superfluid weight at integer filling (size scaling exponent is near one), but the Fourier transform of the polarization amplitude behaves in a similar way to the result of exact diagonalization, with a peak at small hopping, and suddenly decreasing at the insulator-superfluid transition. On the other hand, exact diagonalization studies result in a finite spread of the total position which increases with the size of the system. In the superfluid phase the size scaling exponent is two as expected. Importantly, our work addresses the ambiguities that arise in the calculation of the superfluid weight in variational calculations, and we comment on the prediction of Anderson about the superfluid response of the model at integer filling."

In a conventional electron spin resonance (ESR) spectrometer based on the inductive detection method, the paramagnetic spins precess in an external magnetic field B0 radiating weak microwave signals into a resonant cavity which are subsequently amplified and measured. Despite its widespread use, ESR spectroscopy has limited sensitivity, and large amounts of spins are necessary to accumulate sufficient signal. Most conventional ESR spectrometers operate at room temperature and employ three-dimensional cavities. At X-band, they require approximately 10^13 spins to obtain sufficient signal in a single echo [1]. Enhancing this sensitivity to smaller spin ensembles and eventually the single spin limit is highly desirable.

Exploiting recent progress in circuit-quantum electrodynamics, we have combined high quality factor superconducting micro-resonators and noise-less Josephson Parametric Amplifiers to perform ESR spectroscopy at millikelvin temperatures, reaching a new regime where the sensitivity is limited by the quantum fluctuations of the microwave field. Quantum fluctuations of the field also affect directly the spin dynamics via Purcell effect : spin relaxation occurs dominantly by spontaneous emissions of microwave photons. Based on these principles [2-4], we first show an unprecedented measurement sensitivity of 10 spins/sqrt(Hz) for unit SNR in an inductive-detection ESR with an ensemble of Bismuth donors in Silicon [5]. This high sensitivity enables us to characterize the coherence properties of an ensemble of donors in close proximity ( 50- 100 nm) to the silicon surface, with spatial resolution. We identify surface magnetic and electric noise as the main decoherence sources in our device. At the so-called "clock transition", the coherence time approaches 1s, which is the longest reported for an electron spin close to a surface [6].

[1] A. Schweiger and G. Jeschke, Principles of pulse electron paramagnetic resonance (Oxford University Press, 2001).
[2] P. Haikka, Y. Kubo, A. Bienfait, P. Bertet, K. Moelmer, Phys. Rev. A 95, 022306 (2017).
[3] A. Bienfait, J. Pla, Y. Kubo, M. Stern, X. Zhou, C.C. Lo,C.Weis, T. Schenkel, M. Thewalt, D. Vion, D. Esteve, B. Julsgaard, K. Moelmer, J. Morton, and P. Bertet, Nature Nanotechnology 11, 253 (2015).
[4] S. Probst, A. Bienfait, P. Campagne-Ibarcq, J. J. Pla, B. Albanese, J. F. Da SilvaBarbosa, T. Schenkel, D. Vion, D. Esteve, K. Moelmer, J. J. L. Morton, R. Heeres, P.Bertet, Appl. Phys. Lett. 111, 202604 (2017)
[5] V. Ranjan et. al., in preparation (2019)
[6] V. Ranjan et. al., in preparation (2019)

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