*Phys Rev Lett ; 125(21): 210505, 2020 Nov 20.*

##### RESUMEN

We report long coherence times (up to 300 ms) for near-surface bismuth donor electron spins in silicon coupled to a superconducting microresonator, biased at a clock transition. This enables us to demonstrate the partial absorption of a train of weak microwave fields in the spin ensemble, their storage for 100 ms, and their retrieval, using a Hahn-echo-like protocol. Phase coherence and quantum statistics are preserved in the storage.

*J Magn Reson ; 310: 106662, 2020 Jan.*

##### RESUMEN

In EPR, spin relaxation is typically governed by interactions with the lattice or other spins. However, it has recently been shown that given a sufficiently strong spin-resonator coupling and high resonator quality factor, the spontaneous emission of microwave photons from the spins into the resonator can become the main relaxation mechanism, as predicted by Purcell. With increasing attention on the use of microresonators for EPR to achieve high spin-number sensitivity it is important to understand how this novel regime influences measured EPR signals, for example the amplitude and temporal shape of the spin-echo. We study this regime theoretically and experimentally, using donor spins in silicon, under different conditions of spin-linewidth and coupling homogeneity. When the spin-resonator coupling is distributed inhomogeneously, we find that the effective spin-echo relaxation time measured in a saturation recovery sequence strongly depends on the parameters for the detection echo. When the spin linewidth is larger than the resonator bandwidth, the different Fourier components of the spin echo relax with different characteristic times - due to the role of the resonator in driving relaxation - which results in the temporal shape of the echo becoming dependent on the repetition time of the experiment.

*Phys Rev Lett ; 120(16): 167701, 2018 Apr 20.*

##### RESUMEN

We experimentally study the coupling of group V donor spins in silicon to mechanical strain, and measure strain-induced frequency shifts that are linear in strain, in contrast to the quadratic dependence predicted by the valley repopulation model (VRM), and therefore orders of magnitude greater than that predicted by the VRM for small strains |Ïµ|<10^{-5}. Through both tight-binding and first principles calculations we find that these shifts arise from a linear tuning of the donor hyperfine interaction term by the hydrostatic component of strain and achieve semiquantitative agreement with the experimental values. Our results provide a framework for making quantitative predictions of donor spins in silicon nanostructures, such as those being used to develop silicon-based quantum processors and memories. The strong spin-strain coupling we measure (up to 150 GHz per strain, for Bi donors in Si) offers a method for donor spin tuning-shifting Bi donor electron spins by over a linewidth with a hydrostatic strain of order 10^{-6}-as well as opportunities for coupling to mechanical resonators.

*Nature ; 531(7592): 74-7, 2016 Mar 03.*

##### RESUMEN

Spontaneous emission of radiation is one of the fundamental mechanisms by which an excited quantum system returns to equilibrium. For spins, however, spontaneous emission is generally negligible compared to other non-radiative relaxation processes because of the weak coupling between the magnetic dipole and the electromagnetic field. In 1946, Purcell realized that the rate of spontaneous emission can be greatly enhanced by placing the quantum system in a resonant cavity. This effect has since been used extensively to control the lifetime of atoms and semiconducting heterostructures coupled to microwave or optical cavities, and is essential for the realization of high-efficiency single-photon sources. Here we report the application of this idea to spins in solids. By coupling donor spins in silicon to a superconducting microwave cavity with a high quality factor and a small mode volume, we reach the regime in which spontaneous emission constitutes the dominant mechanism of spin relaxation. The relaxation rate is increased by three orders of magnitude as the spins are tuned to the cavity resonance, demonstrating that energy relaxation can be controlled on demand. Our results provide a general way to initialize spin systems into their ground state and therefore have applications in magnetic resonance and quantum information processing. They also demonstrate that the coupling between the magnetic dipole of a spin and the electromagnetic field can be enhanced up to the point at which quantum fluctuations have a marked effect on the spin dynamics; as such, they represent an important step towards the coherent magnetic coupling of individual spins to microwave photons.

*Nat Nanotechnol ; 11(3): 253-7, 2016 Mar.*

##### RESUMEN

The detection and characterization of paramagnetic species by electron spin resonance (ESR) spectroscopy is widely used throughout chemistry, biology and materials science, from in vivo imaging to distance measurements in spin-labelled proteins. ESR relies on the inductive detection of microwave signals emitted by the spins into a coupled microwave resonator during their Larmor precession. However, such signals can be very small, prohibiting the application of ESR at the nanoscale (for example, at the single-cell level or on individual nanoparticles). Here, using a Josephson parametric microwave amplifier combined with high-quality-factor superconducting microresonators cooled at millikelvin temperatures, we improve the state-of-the-art sensitivity of inductive ESR detection by nearly four orders of magnitude. We demonstrate the detection of 1,700 bismuth donor spins in silicon within a single Hahn echo with unit signal-to-noise ratio, reduced to 150 spins by averaging a single Carr-Purcell-Meiboom-Gill sequence. This unprecedented sensitivity reaches the limit set by quantum fluctuations of the electromagnetic field instead of thermal or technical noise, which constitutes a novel regime for magnetic resonance. The detection volume of our resonator is â¼ 0.02 nl, and our approach can be readily scaled down further to improve sensitivity, providing a new versatile toolbox for ESR at the nanoscale.

##### Asunto(s)

Amplificadores Electrónicos , Espectroscopía de Resonancia por Spin del Electrón/instrumentación , Espectroscopía de Resonancia por Spin del Electrón/métodos , Microquímica/instrumentación , Nanopartículas/análisis , Nanopartículas/química , Aire Acondicionado/instrumentación , Síndrome de Creutzfeldt-Jakob , Diseño de Equipo , Análisis de Falla de Equipo , Microondas , Miniaturización , Teoría Cuántica , Reproducibilidad de los Resultados , Sensibilidad y Especificidad , Relación Señal-Ruido*Science ; 349(6253): 1199-202, 2015 Sep 11.*

##### RESUMEN

Coherent control of quantum states has been demonstrated in a variety of superconducting devices. In all of these devices, the variables that are manipulated are collective electromagnetic degrees of freedom: charge, superconducting phase, or flux. Here we demonstrate the coherent manipulation of a quantum system based on Andreev bound states, which are microscopic quasi-particle states inherent to superconducting weak links. Using a circuit quantum electrodynamics setup, we performed single-shot readout of this Andreev qubit. We determined its excited-state lifetime and coherence time to be in the microsecond range. Quantum jumps and parity switchings were observed in continuous measurements. In addition to having possible quantum information applications, such Andreev qubits are a test-bed for the physics of single elementary excitations in superconductors.

*Phys Rev Lett ; 113(12): 123601, 2014 Sep 19.*

##### RESUMEN

We present measurements of superconducting flux qubits embedded in a three dimensional copper cavity. The qubits are fabricated on a sapphire substrate and are measured by coupling them inductively to an on-chip superconducting resonator located in the middle of the cavity. At their flux-insensitive point, all measured qubits reach an intrinsic energy relaxation time in the 6-20 µs range and a pure dephasing time comprised between 3 and 10 µs. This significant improvement over previous works opens the way to the coherent coupling of a flux qubit to individual spins.

*Phys Rev Lett ; 110(4): 047001, 2013 Jan 25.*

##### RESUMEN

We measure the quantum fluctuations of a pumped nonlinear resonator using a superconducting artificial atom as an in situ probe. The qubit excitation spectrum gives access to the frequency and amount of excitation of the intracavity field fluctuations, from which we infer its effective temperature. These quantities are found to be in agreement with theoretical predictions; in particular, we experimentally observe the phenomenon of quantum heating.

*Phys Rev Lett ; 108(5): 057002, 2012 Feb 03.*

##### RESUMEN

We report the characterization of a two-qubit processor implemented with two capacitively coupled tunable superconducting qubits of the transmon type, each qubit having its own nondestructive single-shot readout. The fixed capacitive coupling yields the sqrt[iSWAP] two-qubit gate for a suitable interaction time. We reconstruct by state tomography the coherent dynamics of the two-bit register as a function of the interaction time, observe a violation of the Bell inequality by 22 standard deviations after correcting readout errors, and measure by quantum process tomography a gate fidelity of 90%.

*Phys Rev Lett ; 107(22): 220501, 2011 Nov 25.*

##### RESUMEN

We report the experimental realization of a hybrid quantum circuit combining a superconducting qubit and an ensemble of electronic spins. The qubit, of the transmon type, is coherently coupled to the spin ensemble consisting of nitrogen-vacancy centers in a diamond crystal via a frequency-tunable superconducting resonator acting as a quantum bus. Using this circuit, we prepare a superposition of the qubit states that we store into collective excitations of the spin ensemble and retrieve back into the qubit later on. These results constitute a proof of concept of spin-ensemble based quantum memory for superconducting qubits.

*Phys Rev Lett ; 106(21): 217005, 2011 May 27.*

##### RESUMEN

We explore the photonic (bright) side of the dynamical Coulomb blockade (DCB) by measuring the radiation emitted by a dc voltage-biased Josephson junction embedded in a microwave resonator. In this regime Cooper pair tunneling is inelastic and associated with the transfer of an energy 2eV into the resonator modes. We have measured simultaneously the Cooper pair current and the photon emission rate at the resonance frequency of the resonator. Our results show two regimes, in which each tunneling Cooper pair emits either one or two photons into the resonator. The spectral properties of the emitted radiation are accounted for by an extension to DCB theory.

*Phys Rev Lett ; 106(16): 167002, 2011 Apr 22.*

##### RESUMEN

We have performed spectroscopic measurements of a superconducting qubit dispersively coupled to a nonlinear resonator driven by a pump microwave field. Measurements of the qubit frequency shift provide a sensitive probe of the intracavity field, yielding a precise characterization of the resonator nonlinearity. The qubit linewidth has a complex dependence on the pump frequency and amplitude, which is correlated with the gain of the nonlinear resonator operated as a small-signal amplifier. The corresponding dephasing rate is found to be close to the quantum limit in the low-gain limit of the amplifier.

*Phys Rev Lett ; 105(14): 140502, 2010 Oct 01.*

##### RESUMEN

We report the realization of a quantum circuit in which an ensemble of electronic spins is coupled to a frequency tunable superconducting resonator. The spins are nitrogen-vacancy centers in a diamond crystal. The achievement of strong coupling is manifested by the appearance of a vacuum Rabi splitting in the transmission spectrum of the resonator when its frequency is tuned through the nitrogen-vacancy center electron spin resonance.

*Phys Rev Lett ; 99(18): 187005, 2007 Nov 02.*

##### RESUMEN

The voltage oscillations which occur in an ideally current-biased Josephson junction were proposed to make a current standard for metrology. We demonstrate similar oscillations in a more complex Josephson circuit derived from the Cooper pair box: the quantronium. When a constant current I is injected in the gate capacitor of this device, oscillations develop at the frequency f(B)=I/2e, with e the electron charge. We detect these oscillations through the sidebands induced at multiples of f(B) in the spectrum of a microwave signal reflected on the circuit, up to currents I exceeding 100 pA. We discuss the potential interest of this current-to-frequency conversion experiment for metrology.

*Phys Rev Lett ; 95(25): 257002, 2005 Dec 16.*

##### RESUMEN

We have studied the dephasing of a superconducting flux qubit coupled to a dc-SQUID based oscillator. By varying the bias conditions of both circuits we were able to tune their effective coupling strength. This allowed us to measure the effect of such a controllable and well-characterized environment on the qubit coherence. We can quantitatively account for our data with a simple model in which thermal fluctuations of the photon number in the oscillator are the limiting factor. In particular, we observe a strong reduction of the dephasing rate whenever the coupling is tuned to zero. At the optimal point we find a large spin-echo decay time of .

*Nature ; 431(7005): 159-62, 2004 Sep 09.*

##### RESUMEN

In the emerging field of quantum computation and quantum information, superconducting devices are promising candidates for the implementation of solid-state quantum bits (qubits). Single-qubit operations, direct coupling between two qubits and the realization of a quantum gate have been reported. However, complex manipulation of entangled states-such as the coupling of a two-level system to a quantum harmonic oscillator, as demonstrated in ion/atom-trap experiments and cavity quantum electrodynamics-has yet to be achieved for superconducting devices. Here we demonstrate entanglement between a superconducting flux qubit (a two-level system) and a superconducting quantum interference device (SQUID). The latter provides the measurement system for detecting the quantum states; it is also an effective inductance that, in parallel with an external shunt capacitance, acts as a harmonic oscillator. We achieve generation and control of the entangled state by performing microwave spectroscopy and detecting the resultant Rabi oscillations of the coupled system.

*Phys Rev Lett ; 89(20): 200402, 2002 Nov 11.*

##### RESUMEN

We have measured the complete Wigner function W of the vacuum and of a single-photon state for a field stored in a high-Q cavity. This experiment implements the direct Lutterbach and Davidovich method [L. G. Lutterbach and L. Davidovich, Phys. Rev. Lett. 78, 2547 (1997)]] and is based on the dispersive interaction of a single circular Rydberg atom with the cavity field. The nonclassical nature of the single-photon field is exhibited by a region of negative W values. Extensions to other nonclassical cavity field states are discussed.

*Phys Rev Lett ; 88(14): 143601, 2002 Apr 08.*

##### RESUMEN

A two-photon Fock state is prepared in a cavity sustaining a "source mode" and a "target mode," with a single circular Rydberg atom. In a third-order Raman process, the atom emits a photon in the target while scattering one photon from the source into the target. The final two-photon state is probed by measuring by Ramsey interferometry the cavity light shifts induced by the target field on the same atom. Extensions to other multiphoton processes and to a new type of micromaser are briefly discussed.

*Phys Rev Lett ; 87(3): 037902, 2001 Jul 16.*

##### RESUMEN

Following a recent proposal by S. B. Zheng and G. C. Guo [Phys. Rev. Lett. 85, 2392 (2000)], we report an experiment in which two Rydberg atoms crossing a nonresonant cavity are entangled by coherent energy exchange. The process, mediated by the virtual emission and absorption of a microwave photon, is characterized by a collision mixing angle 4 orders of magnitude larger than for atoms colliding in free space with the same impact parameter. The final entangled state is controlled by adjusting the atom-cavity detuning. This procedure, essentially insensitive to thermal fields and to photon decay, opens promising perspectives for complex entanglement manipulations.

*Nature ; 411(6834): 166-70, 2001 May 10.*

##### RESUMEN

To illustrate the quantum mechanical principle of complementarity, Bohr described an interferometer with a microscopic slit that records the particle's path. Recoil of the quantum slit causes it to become entangled with the particle, resulting in a kind of Einstein-Podolsky-Rosen pair. As the motion of the slit can be observed, the ambiguity of the particle's trajectory is lifted, suppressing interference effects. In contrast, the state of a sufficiently massive slit does not depend on the particle's path; hence, interference fringes are visible. Although many experiments illustrating various aspects of complementarity have been proposed and realized, none has addressed the quantum-classical limit in the design of the interferometer. Here we report an experimental investigation of complementarity using an interferometer in which the properties of one of the beam-splitting elements can be tuned continuously from being effectively microscopic to macroscopic. Following a recent proposal, we use an atomic double-pulse Ramsey interferometer, in which microwave pulses act as beam-splitters for the quantum states of the atoms. One of the pulses is a coherent field stored in a cavity, comprising a small, adjustable mean photon number. The visibility of the interference fringes in the final atomic state probability increases with this photon number, illustrating the quantum to classical transition.