We use nominally forbidden electron-nuclear spin transitions in nitrogen-vacancy (NV) centers in diamond to demonstrate coherent manipulation of a nuclear spin ensemble using microwave fields at room temperature. We show that employing an off-axis magnetic field with a modest amplitude($\approx$ 0.01 T) at an angle with respect to the NV natural quantization axes is enough to tilt the direction of the electronic spins, and enable efficient spin exchange with the nitrogen nuclei of the NV center. We could then demonstrate fast Rabi oscillations on electron-nuclear spin exchanging transitions, coherent population trapping and polarization of nuclear spin ensembles in the microwave regime. Coupling many electronic spins of NV centers to their intrinsic nuclei offers full scalability with respect to the number of controllable spins and provides prospects for transduction. In particular, the technique could be applied to long-lived storage of microwave photons and to the coupling of nuclear spins to mechanical oscillators in the resolved sideband regime.
Quantum microwave transmission is key to realizing modular superconducting quantum computers and distributed quantum networks. A large number of incoherent photons are thermally generated within the microwave frequency spectrum. The closeness of the transmitted quantum state to the source-generated quantum state at the input of the transmission link (measured by the transmission fidelity) degrades due to the presence of the incoherent photons. Hence, high-fidelity quantum microwave transmission has long been considered to be infeasible without refrigeration [3,4]. In this study, we propose a n…
We investigate numerically a single-pulse implementation of a quantum Control-Not (CN) gate for an ensemble of Ising spin systems at room temperature. For an ensemble of four-spin ``molecules'' we simulate the time-evolution of the density matrix, for both digital and superpositional initial conditions. Our numerical calculations confirm the feasibility of implementation of quantum CN gate in this system at finite temperature, using electromagnetic $π$-pulse.
We report experimental generation of non-classically correlated photon pairs from collective emission in a room-temperature atomic vapor cell. The nonclassical feature of the emission is demonstrated by observing a violation of the Cauchy-Schwarz inequality. Each pair of correlated photons are separated by a controllable time delay up to 2 microseconds. This experiment demonstrates an important step towards the realization of the Duan-Lukin-Cirac-Zoller scheme for scalable long-distance quantum communication.
We report a demonstration of the hallmark concept of quantum optics: periodic collapse and revival of quantum coherence (QCR) in a room temperature ensemble of quantum dots (QD). Control over quantum states, inherent to QCR, together with the dynamical QD properties present an opportunity for practical room temperature building blocks of quantum information processing. The amplitude decay of QCR is dictated by the QD homogeneous linewidth, thus, enabling its extraction in a double-pulse Ramsey-type experiment. The more common photon echo technique was also invoked and yielded the same linewidt…
We show that pairs of atoms optically excited to the Rydberg states can strongly interact with each other via effective long-range dipole-dipole or van der Waals interactions mediated by their non-resonant coupling to a common microwave field mode of a superconducting coplanar waveguide cavity. These cavity mediated interactions can be employed to generate single photons and to realize in a scalable configuration a universal phase gate between pairs of single photon pulses propagating or stored in atomic ensembles in the regime of electromagnetically induced transparency.
Experiments have reported the entanglement of two spatially separated macroscopic atomic ensembles at room temperature (Krauter et al 2011 Phys. Rev. Lett. 107 080503; Julsgaard et al 2001 Nature 413 400). We show how an Einstein-Podolsky-Rosen (EPR) paradox is realizable with this experiment. Our proposed test involves violation of an inferred Heisenberg uncertainty principle, which is a sufficient condition for an EPR paradox. This is a stronger test of nonlocality than entanglement. Our proposal would enable the first definitive confirmation of quantum EPR paradox correlations between two m…
We propose a multi-mode quantum memory protocol able to store the quantum state of the field in a microwave resonator into an ensemble of electronic spins. The stored information is protected against inhomogeneous broadening of the spin ensemble by spin-echo techniques resulting in memory times orders of magnitude longer than previously achieved. By calculating the evolution of the first and second moments of the spin-cavity system variables for realistic experimental parameters, we show that a memory based on NV center spins in diamond can store a qubit encoded on the |0> and |1> Fock states …
A protocol is discussed which allows one to realize a transducer for single photons between the optical and the microwave frequency range. The transducer is a spin ensemble, where the individual emitters possess both an optical and a magnetic-dipole transition. Reversible frequency conversion is realized by combining optical photon storage, by means of EIT, with the controlled switching of the coupling between the magnetic-dipole transition and a superconducting qubit, which is realized by means of a microwave cavity. The efficiency is quantified by the global fidelity for transferring coheren…
Cavity quantum electrodynamics (C-QED) effects, such as Rabi splitting, Rabi oscillations and superradiance, have been demonstrated with nitrogen vacancy center spins in diamond in microwave resonators at cryogenic temperature. In this article we explore the possibility to realize strong collective coupling and the resulting C-QED effects with ensembles of spins at room temperature. Thermal excitation of the individual spins by the hot environment leads to population of collective Dicke states with low symmetry and a reduced collective spin-microwave field coupling. However, we show with simul…
We experimentally demonstrate the temporary removal of thermal photons from a microwave mode at 1.45 GHz through its interaction with the spin-polarized triplet states of photo-excited pentacene molecules doped within a p-terphenyl crystal at room temperature. The crystal functions electromagnetically as a narrow-band cryogenic load, removing photons from the otherwise room-temperature mode via stimulated absorption. The noise temperature of the microwave mode dropped to $50^{+18}_{-32}$ K (as directly inferred by noise-power measurements) while the metal walls of the cavity enclosing the mode…
We report the storage of microwave pulses at the single-photon level in a spin-ensemble memory consisting of $10^{10}$ NV centers in a diamond crystal coupled to a superconducting LC resonator. The energy of the signal, retrieved $100\, μ\mathrm{s}$ later by spin-echo techniques, reaches $0.3\%$ of the energy absorbed by the spins, and this storage efficiency is quantitatively accounted for by simulations. This figure of merit is sufficient to envision first implementations of a quantum memory for superconducting qubits.
NV-ensemble enabled microwave/NV parametric amplifier with optimal driving
Akhiezer Institute for Theoretical Physics, NSC KIPT（阿赫伊泽尔理论物理研究所，NSC KIPT）；U.S. Army DEVCOM Army Research Laboratory（美国陆军DEVCOM陆军研究实验室）；University of Massachusetts at Boston（波士顿马萨诸塞大学）；Education and Research Institute “School of Physics and Technology”, Karazin Kharkiv National University（克拉辛哈尔科夫国立大学“物理与技术学院”教育与研究所）；Massachusetts Institute of Technology（麻省理工学院）；Tulane University（杜兰大学）
We demonstrate trapping of electrons in a millimeter-sized quadrupole Paul trap driven at 1.6~GHz in a room-temperature ultra-high vacuum setup. Cold electrons are introduced into the trap by ionization of atomic calcium via Rydberg states and stay confined by microwave and static electric fields for several tens of milliseconds. A fraction of these electrons remain trapped longer and show no measurable loss for measurement times up to a second. Electronic excitation of the motion reveals secular frequencies which can be tuned over a range of several tens to hundreds of MHz. Operating a simila…
Electron and nuclear spins have good coherence times and an ensemble of spins is a promising candidate for a quantum memory. By employing holographic techniques via field gradients a single ensemble may be used to store many bits of information. Here we present a coherent memory using a pulsed magnetic field gradient, and demonstrate the storage and retrieval of up to 100 weak 10 GHz coherent excitations in collective states of an electron spin ensemble. We further show that such collective excitations in the electron spin can then be stored in nuclear spin states, which offer coherence times …
Raman heterodyne spectroscopy is a powerful tool for characterizing the energy and dynamics of spins. The technique uses an optical pump to transfer coherence from a spin transition to an optical transition where the coherent emission is more easily detected. Here Raman heterodyne spectroscopy is used to probe an isotopically purified ensemble of erbium dopants, in a yttrium orthosilicate (Y$_2$SiO$_5$) crystal coupled to a microwave cavity. Because the erbium electron spin transition is strongly coupled to the microwave cavity, we observed Raman heterodyne signals at the resonant frequencies …
We describe a multi-mode quantum memory for propagating microwave photons that combines a solid-state spin ensemble resonantly coupled to a frequency tunable single-mode microwave cavity. We first show that high efficiency mapping of the quantum state transported by a free photon to the spin ensemble is possible both for strong and weak coupling between the cavity mode and the spin ensemble. We also show that even in the weak coupling limit unit efficiency and faithful retrieval can be obtained through time reversal inhomogeneous dephasing based on spin echo techniques. This is possible provid…
We report the storage and retrieval of a small microwave field from a superconducting resonator into collective excitations of a spin ensemble. The spins are nitrogen-vacancy centers in a diamond crystal. The storage time of the order of 30 ns is limited by inhomogeneous broadening of the spin ensemble.
Lasers have revolutionized optical science and technology, but their microwave counterpart, maser, has not realized its great potential due to its demanding work conditions (high-vacuum for gas maser and liquid-helium temperature for solid-state maser). Room-temperature solid-state maser is highly desirable, but under such conditions the lifetimes of emitters (usually electron spins) are usually too short (~ns) for population inversion. The only room-temperature solid-state maser is based on a pentacene-doped p-terphenyl crystal, which has long spin lifetime (~0.1 ms). This maser, however, ope…
We demonstrate dispersive readout of the spin of an ensemble of Nitrogen-Vacancy centers in a high-quality dielectric microwave resonator at room temperature. The spin state is inferred from the reflection phase of a microwave signal probing the resonator. Time-dependent tracking of the spin state is demonstrated, and is employed to measure the T1 relaxation time of the spin ensemble. Dispersive readout provides a microwave interface to solid state spins, translating a spin signal into a microwave phase shift. We estimate that its sensitivity can outperform optical readout schemes, owing to th…
We propose a protocol to dissipatively cool a room temperature mechanical resonator using a nitrogen-vacancy (NV) center ensemble. The spin ensemble is coupled to the resonator through its orbitally-averaged excited state, which has a spin-strain interaction that has not been previously characterized. We experimentally demonstrate that the spin-strain coupling in the excited state is $13.5\pm0.5$ times stronger than the ground state spin-strain coupling. We then theoretically show that this interaction combined with a high-density spin ensemble enables the cooling of a mechanical resonator fro…
Hybrid non-degenerate parametric amplifier for a microwave cavity mode and an NV ensemble
Akhiezer Institute for Theoretical Physics, NSC KIPT（阿基谢尔理论物理研究所，NSC KIPT）；Advanced Photonics and Electronics Division, U.S. Army DEVCOM Army Research Laboratory（先进光子学与电子学部门，美国陆军DEVCOM陆军研究实验室）；Department of Physics, University of Massachusetts at Boston（马萨诸塞大学波士顿分校物理系）；Education and Research Institute “School of Physics and Technology”, Karazin Kharkiv National University（卡尔齐诺夫哈尔科夫国立大学教育与研究所“物理与技术学院”）；Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology（麻省理工学院电气与计算机工程系）；Department of Physics and Engineering Physics, Tulane University（杜兰大学物理与工程物理系）
Microwave receivers using electromagnetically-induced transparency (EIT) in Rydberg atoms have recently demonstrated improved sensitivities. It is not evident how their state-of-the-art electric field sensitivities compare to those achieved using standard electronic receivers consisting of low-noise amplifiers (LNAs) and mixers. In this paper, we show that conventional room-temperature electronic receivers greatly outperform the best demonstrated sensitivities of room-temperature Rydberg electrometers in standard free-space coupled configurations. However, Rydberg-atom receivers can surpass th…
Recent experiments demonstrated the cooling of a microwave mode of a high-quality dielectric resonator coupled to optically cooled nitrogen-vacancy (NV) spins in diamond. Our recent theoretical study [arXiv:2110.10950] pointed out the cooled NV spins can be used to realize cavity quantum electrodynamics effects (C-QED) at room temperature. In this article, we propose to modify the setup used in a recent diamond maser experiment [Nature 55, 493-496 (2018)], which features a higher spin transition frequency, a lower spin-dephasing rate and a stronger NV spins-resonator coupling, to realize bette…
We theoretically investigate an ensemble of three-level room-temperature atoms in a two-mode optical cavity, focusing on the case of counterpropagating light fields. We find that in the limit of large detunings the problem admits relatively simple and intuitive solutions. When a classical field drives one of the transitions, the system becomes equivalent to an ensemble of two-level atoms with suppressed Doppler broadening. In contrast, when the same transition is driven with a single photon, the system collectively behaves like a single two-level atom. This latter result is particularly releva…
Interfacing superconducting qubits with optical photons requires noise-free microwave-to-optical transducers, a technology currently not realized at the single-photon level. We propose to use four-wave-mixing in an ensemble of cold ytterbium (Yb) atoms prepared in the metastable 'clock' state. The parametric process uses two high-lying Rydberg states for bidirectional conversion between a 10 GHz microwave photon and an optical photon in the telecommunication E-band. To avoid noise photons due to spontaneous emission, we consider continuous operation far detuned from the intermediate states. We…
Probing an electron spin ensemble with squeezed microwave signals
Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften（瓦尔特·迈斯纳研究所，巴伐利亚科学院）；Technical University of Munich, TUM School of Natural Sciences, Physics Department（慕尼黑工业大学，自然科学学院，物理系）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
Rydberg atoms are at the core of an increasing number of experiments, which frequently rely on destructive detection methods, such as field ionization. Here, we present an experimental realization of single-shot non-destructive detection of ensembles of helium Rydberg atoms. We use the dispersive frequency shift of a superconducting microwave cavity interacting with the ensemble. By probing the transmission of the cavity and measuring the change in its phase, we determine the number of Rydberg atoms or the populations of Rydberg quantum states when the ensemble is prepared in a superposition. …
Establishing quantum entanglement between individual nodes is crucial for building large-scale quantum networks, enabling secure quantum communication, distributed quantum computing, enhanced quantum metrology and fundamental tests of quantum mechanics. However, the shared entanglements have been merely observed in either extremely low-temperature or well-isolated systems, which limits the quantum networks for the real-life applications. Here, we report the realization of heralding quantum entanglement between two atomic ensembles at room temperature, where each of them contains billions of mo…
We examine quantum statistics of optical photons emitted from atomic ensembles which are classically driven and simultaneously coupled to a two-level atom via microwave photon exchange. Quantum statistics and correlations are analyzed by calculating second order coherence degree, von Neumann entropy, spin squeezing for multi-particle entanglement, as well as genuine two and three-mode entanglement parameters for steady state and non-equilibrium situations. Coherent transfer of population between the radiation modes and quantum state mapping between the two-level atom and the optical modes are …
We investigate the coupling of an ensemble of phosphorus donors in an isotopically purified $^{28}$Si host lattice interacting with a superconducting coplanar waveguide resonator. The microwave transmission spectrum of the resonator shows a normal mode splitting characteristic for high cooperativity. The evaluated collective coupling strength $g_{\mathrm{eff}}$ is of the same order as the loss rate of the spin system $γ$, indicating the onset of strong coupling. We develop a statistical model to describe the influence of temperature on the coupling strength from $50\,\mathrm{mK}$ to $3.5\,\mat…
We demonstrate the use of high-Q superconducting coplanar waveguide (CPW) microresonators to perform rapid manipulations on a randomly distributed spin ensemble using very low microwave power (400 nW). This power is compatible with dilution refrigerators, making microwave manipulation of spin ensembles feasible for quantum computing applications. We also describe the use of adiabatic microwave pulses to overcome microwave magnetic field ($B_{1}$) inhomogeneities inherent to CPW resonators. This allows for uniform control over a randomly distributed spin ensemble. Sensitivity data are reported …
The T centre, a silicon-native spin-photon interface with telecommunications-band optical transitions and long-lived microwave qubits, offers an appealing new platform for both optical quantum memory and microwave to optical telecommunications band transduction. A wide range of quantum memory and transduction schemes could be implemented on such a platform, with advantages and disadvantages that depend sensitively on the ensemble properties. In this work we characterize T centre spin ensembles to inform device design. We perform the first T ensemble optical depth measurement and calculate the …
Continuous spectral hole burning and spin-level population oscillations are studied in an inhomogeneously broadened diamond-based spin ensemble composed of substitutional nitrogen and nitrogen-vacancy centres created through neutron irradiation and annealing. The burnt spectral features highlight a detuning-dependent homogeneous hole linewidth that is up to three orders of magnitude narrower than the total inhomogeneous ensemble linewidth. Continuous population oscillations are observed to quickly decay beyond a pump and probe detuning of 5 Hz, and are numerically modelled using a five-level s…
We study the nonlinear dynamics of an ensemble of cold trapped atoms with a hyperfine transition magnetically coupled to a resonant microwave cavity mode. Despite the minute single atom coupling one obtains strong coupling between collective hyperfine qubits and microwave photons enabling coherent transfer of an excitation between the long lived atomic qubit state and the mode. Evidence of strong coupling can be obtained from the cavity transmission spectrum even at finite thermal photon number. The system makes it possible to study further prominent collective phenomena such as superradiant d…
We demonstrate the strong coupling between an electron spin ensemble and a three-dimensional cavity in a reflection geometry. We also find that an anticrossing in the cavity/spin spectrum can be observed under conditions that the collective coupling strength $g_c$ is smaller than the spin linewidth $γ_s$ or the cavity linewidth. We identify a ratio of $g_c$ to $γ_s$ ($g_c/γ_s >$ 0.64) as a condition to observe a splitting in the cavity frequency. Finally, we confirm that $g_c$ scales with $\sqrt{N}$, where $N$ is the number of polarized spins.
There has been much recent interest in extending the technique of magnetic resonance imaging (MRI) down to the level of single spins with sub-optical wavelength resolution. However, the signal to noise ratio for images of individual spins is usually low and this necessitates long acquisition times and low temperatures to achieve high resolution. An exception to this is the nitrogen-vacancy (NV) color center in diamond whose spin state can be detected optically at room temperature. Here we apply MRI to magnetically equivalent NV spins in order to resolve them with resolution well below the opti…
We introduce a microwave-assisted spectroscopy technique to determine the relative concentrations of nitrogen vacancy (NV) centers in diamond that are negatively-charged (NV${}^-$) and neutrally-charged (NV${}^0$), and present its application to studying spin-dependent ionization in NV ensembles and enhancing NV-magnetometer sensitivity. Our technique is based on selectively modulating the NV${}^-$ fluorescence with a spin-state-resonant microwave drive to isolate, in-situ, the spectral shape of the NV${}^-$ and NV${}^0$ contributions to an NV-ensemble sample's fluorescence. As well as serving…
We study ensembles of Rydberg atoms in a confined electromagnetic environment such as provided by a microwave cavity. The competition between standard free space Ising type and cavity-mediated interactions leads to the emergence of different regimes where the particle-particle couplings range from the typical van der Waals $r^{-6}$ behavior to $r^{-3}$ and to $r$-independence. We apply a Ramsey spectroscopic technique to map the two-body interactions into a characteristic signal such as intensity and contrast decay curves. As opposed to previous treatments requiring high-densities for consider…
We analyze the magnetic dipole coupling of an ensemble of spins to a superconducting microwave stripline structure, incorporating a Josephson junction based transmon qubit. We show that this system is described by an embedded Jaynes-Cummings model: in the strong coupling regime, collective spin-wave excitations of the ensemble of electrons pick up the nonlinearity of the cavity mode, such that the two lowest eigenstates of the coupled spin-wave + microwave-cavity + Josephson-junction system define a hybrid two-level system. The proposal described here enables the use of spin ensembles as qubit…
We achieve the strong coupling regime between an ensemble of phosphorus donor spins in a highly enriched $^{28}$Si crystal and a 3D dielectric resonator. Spins were polarized beyond Boltzmann equilibrium using spin selective optical excitation of the no-phonon bound exciton transition resulting in $N$ = $3.6\cdot10^{13}$ unpaired spins in the ensemble. We observed a normal mode splitting of the spin ensemble-cavity polariton resonances of 2$g\sqrt{N}$ = 580 kHz (where each spin is coupled with strength $g$) in a cavity with a quality factor of 75,000 ($γ\ll κ\approx$ 60 kHz where $γ$ and $κ$ a…
In recent years the interest in studying interactions of Rydberg atoms or ensembles thereof with optical and microwave frequency fields has steadily increased, both in the context of basic research and for potential applications in quantum information processing. We present measurements of the dispersive interaction between an ensemble of helium atoms in the 37s Rydberg state and a single resonator mode by extracting the amplitude and phase change of a weak microwave probe tone transmitted through the cavity. The results are in quantitative agreement with predictions made on the basis of the d…
