We show experimentally and describe theoretically how a conventional magnetic resonance Hahn echo sequence can lead to a self-stimulated pulse echo train when an inhomogeneously broadened spin ensemble is coupled to a resonator. Effective strong coupling between the subsystems assures that the first Hahn echo can act as a refocussing pulse on the spins, leading to self-stimulated secondary echoes. Within the framework of mean field theory, we show that this process can continue multiple times leading to a train of echoes. We introduce an analytical model that explains the shape of the first echo and numerical results that account well for the experimentally observed shape and strength of the echo train and provides insights into the collective effects involved.
We derive composite pulse sequences that achieve high-fidelity excitation of two-state systems in an optically dense, inhomogeneously broadened ensemble. The composite pulses are resistant to distortions due to the back-action of the medium they propagate in and are able to create high-fidelity inversion to optical depths $αz>10$. They function well with smooth pulse shapes used for coherent control of optical atomic transitions in quantum computation and communication. They are an intermediary solution between single $π$-pulse excitation schemes and adiabatic passage schemes, being far more e…
We study collective effects in an inhomogeneously broadened ensemble of two-level emitters coupled to an optical cavity with narrow linewidth. Using second order mean field theory we find that the emitters within a few times the cavity linewidth exhibit synchronous behaviour and undergo collective Rabi oscillations. Under proper conditions, the synchronized oscillations give rise to a modulated intracavity field which can excite emitters detuned by many linewidths from the cavity resonance. To study the synchronization in further detail, we simplify the model and consider two ensembles and stu…
The creation of single collective excitations in atomic ensembles via spontaneous Raman emission plays a key role in several quantum communication protocols, starting with the seminal DLCZ protocol [L.-M.Duan, M.D. Lukin, J.I. Cirac, and P. Zoller, Nature {\bf 414}, 413 (2001).] This process is usually analyzed theoretically under the assumptions that the write laser pulse inducing the Raman transition is far off-resonance, and that the atomic ensemble is only homogeneously broadened. Here we study the impact of near-resonance excitation for inhomogeneously broadened ensembles on the collectiv…
We address the propagation of a single photon pulse with two polarization components, i.e., a polarization qubit, in an inhomogeneously broadened "phaseonium" Λ-type three-level medium. We combine some of the non-trivial propagation effects characteristic for this kind of coherently prepared systems and the controlled reversible inhomogeneous broadening technique to propose several quantum information processing applications, such as a protocol for polarization qubit filtering and sieving as well as a tunable polarization beam splitter. Moreover, we show that, by imposing a spatial variation o…
We present a method for performing quantum state reconstruction on qubits and qubit registers in the presence of decoherence and inhomogeneous broadening. The method assumes only rudimentary single qubit rotations as well as knowledge of decoherence and loss mechanisms. We show that full state reconstruction is possible even in the case where single qubit rotations may only be performed imperfectly. Furthermore we show that for ensemble quantum computing proposals, quantum state reconstruction is possible even if the ensemble experiences inhomogeneous broadening and if only imperfect qubit man…
Here we propose a solid-state quantum memory that does not require spectral holeburning, instead using strong rephasing pulses like traditional photon echo techniques. The memory uses external broadening fields to reduce the optical depth and so switch off the collective atom-light interaction when desired. The proposed memory should allow operation with reasonable efficiency in a much broader range of material systems, for instance Er3+ doped crystals which have a transition at 1.5 um. We present analytic theory supported by numerical calculations and initial experiments.
In large ensembles of identical atoms or spins, the interaction with a mode of the electromagnetic radiation field concentrates in a single superradiant degree of freedom with a collectively enhanced coupling. Given a controllable inhomogeneous broadening, such ensembles may be used for multi-mode storage of quantum states of the radiation field with applications in quantum communication networks and quantum computers. In this paper we analyze how the width and shape of the inhomogeneous broadening influence the collective enhancement and the dynamics of the cavity-ensemble system with focus o…
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 …
We propose and analyze a scheme for "on demand" creation of coherent superposition of meta-stable states in a tripod-structured atom using frequency-chirped laser pulses. Negligible excitation of the atoms during the creation of the superposition states is a priority in our consideration. The underlying physics of the scheme is explained using the formalism of adiabatic states. By numerically solving master equation for the density matrix operator, we analyze the influence of the spontaneous decay and transverse relaxation on the efficiency of the creation of superposition states. We show that…
Theoretical studies of superradiant lasing on optical clock transitions predict a superb frequency accuracy and precision closely tied to the bare atomic linewidth. Such a superradiant laser is also robust against cavity fluctuations when the spectral width of the lasing mode is much larger than that of the atomic medium. Recent predictions suggest that this unique feature persists even for a hot and thus strongly broadened ensemble, provided the effective atom number is large enough. Here we use a second-order cumulant expansion approach to study the power, linewidth and lineshifts of such a …
The proposal for quantum computing with rare-earth-ion qubits in inorganic crystals makes use of the inhomogeneous broadening of optical transitions in the ions to associate individual qubits with ions responding to radiation in selected frequency channels. We show that a class of Gaussian composite pulses and complex sech pulses provide accurate qubit pi-rotations, which are at the same time channel selective on a 5 MHz frequency scale and tolerant to 0.5 MHz deviations of the transition frequency of ions within a single channel. Rotations in qubit space of arbitrary angles and phases are pro…
We study, theoretically and experimentally, electromagnetically induced transparency (EIT) in two different solid-state systems. Unlike many implementations in homogeneously broadened media, these systems exhibit inhomogeneous broadening of their optical and spin transitions typical of solid-state materials. We observe EIT lineshapes typical of atomic gases, including a crossover into the regime of Autler-Townes splitting, but with the substitution of the inhomogeneous widths for the homogeneous values. We obtain quantitative agreement between experiment and theory for the width of the transpa…
We extend our earlier investigations [Opt. Commun. {\bf 179}, 97 (2000)] on the enhancement of magneto-optical rotation (MOR) to include inhomogeneous broadening. We introduce a control field that counter-propagates with respect to the probe field. We derive analytical results for the susceptibilities corresponding to the two circular polarization components of the probe field. From the analytical results we identify and numerically demonstrate the region of parameters where significantly large magneto-optical rotation (MOR) can be obtained. From the numerical results we isolate the significan…
We propose a method to achieve significant optical signal delays exploiting the effect of Autler-Townes splitting in an inhomogeneously broadened quantum dot medium. The absorption and slow-down effects are compared for three schemes i.e. $Ξ$, V and $Λ$, corresponding to different excitation configurations. Qualitative differences of the V-scheme compared to the $Ξ$- and $Λ$-scheme are found, which show that features of Autler-Townes splitting are only revealed in the V-scheme. The underlying physical mechanisms causing this discrepancy are analyzed and discussed. Finally we compare field prop…
Bad cavity lasers are experiencing renewed interest in the context of active optical frequency standards, due to their enhanced robustness against fluctuations of the laser cavity. The gain medium would consist of narrow-linewidth atoms, either trapped inside the cavity or intersecting the cavity mode dynamically. A series of effects like the atoms finite velocity distribution, atomic interactions, or interactions of realistic multilevel atoms with auxiliary or stray fields can lead to an inhomogeneous broadening of the atomic gain profile. This causes the emergence of instable regimes of lase…
Ensembles of quantum mechanical spins offer a promising platform for quantum memories, but proper functionality requires accurate control of unavoidable system imperfections. We present an efficient control scheme for a spin ensemble strongly coupled to a single-mode cavity based on a set of Volterra equations relying solely on weak classical control pulses. The viability of our approach is demonstrated in terms of explicit storage and readout sequences that will serve as a starting point towards the realization of more demanding full quantum mechanical optimal control schemes.
Electromagnetically induced transparency (EIT) is a phenomenon that can provide strong and robust interfacing between optical signals and quantum coherence of electronic spins. In its archetypical form, mainly explored with atomic media, it uses a (near-)homogeneous ensemble of three-level systems, in which two low-energy spin-1/2 levels are coupled to a common optically excited state. We investigate the implementation of EIT with c-axis divacancy color centers in silicon carbide. While this material has attractive properties for quantum device technologies with near-IR optics, implementing EI…
Electromagnetically induced transparency (EIT) has mainly been modelled for three-level systems. In particular, a considerable interest has been dedicated to the Lambda-configuration, with two ground states and one excited state. However, in the alkali-metal atoms, which are commonly used, hyperfine interaction in the excited state introduces several levels which simultaneously participate in the scattering process. When the Doppler broadening is comparable with the hyperfine splitting in the upper state, the three-level Lambda model does not reproduce the experimental results. Here we theoret…
We describe how stimulated Raman adiabatic passage (STIRAP) can be applied to create spectral holes in an inhomogeneously broadened system. Due to the robustness of STIRAP, our proposal guarantees high flexibility and accuracy and, at variance with traditional spectral hole burning techniques, it may require substantially less time resources since it does not rely upon the spontaneous decay of an intermediate excited state. We investigate the effects on the scheme of dephasing and dissipation as well as of unintentional driving of undesired transitions due to a finite splitting of the initial …
A very promising recent trend in applied quantum physics is to combine the advantageous features of different quantum systems into what is called "hybrid quantum technology". One of the key elements in this new field will have to be a quantum memory enabling to store quanta over extended periods of time. Systems that may fulfill the demands of such applications are comb-shaped spin ensembles coupled to a cavity. Due to the decoherence induced by the inhomogeneous ensemble broadening, the storage time of these quantum memories is, however, still rather limited. Here we demonstrate how to overco…
We study the dynamics of a spin ensemble strongly coupled to a single-mode resonator driven by external pulses. When the mean frequency of the spin ensemble is in resonance with the cavity mode, damped Rabi oscillations are found between the spin ensemble and the cavity mode which we describe very accurately, including the dephasing effect of the inhomogeneous spin broadening. We demonstrate that a precise knowledge of this broadening is crucial both for a qualitative and a quantitative understanding of the temporal spin-cavity dynamics. On this basis we show that coherent oscillations between…
Specific features of nonlinear interference processes at quantum transitions in near- and fully-resonant optically-dense Doppler-broadened medium are studied. The feasibility of overcoming of the fundamental limitation on a velocity-interval of resonantly coupled molecules imposed by the Doppler effect is shown based on quantum coherence. This increases the efficiency of nonlinear-optical processes in atomic and molecular gases that possess the most narrow and strongest resonances. The possibility of all-optical switching of the medium to opaque or, alternatively, to absolutely transparent, or…
Quantum coherence control is presented for wavelength convertible quantum memory in a double-lambda-type solid ensemble whose spin states are inhomogeneously broadened. Unlike typical atomic media whose spin decay is homogeneous, a spin inhomogeneously broadened solid ensemble requires a counter-intuitive access in the quantum coherence control to avoid spontaneous emission-caused quantum noises. Such quantum coherence control in a solid ensemble results in a near perfect retrieval efficiency and is applicable to ultralong photon storage up to the spin phase relaxation time. Here, the basic ph…
Pulse propagation is considered in an inhomogeneously broadened medium of three-level atoms in a V-configuration, dressed by a counter-propagating pump pulse. A significant signal slowdown is demonstrated in this of the three frequency windows of a reduced absorption and a steep normal dispersion, which is due to a cross-over resonance. Particular properties of the group index in the vicinity of such a resonance are demonstrated in the case of closely spaced upper levels.
Using double optical Raman rephasing, an inversion-free resonant Raman echo is studied in an inhomogeneously broadened spin ensemble of a solid medium, where the Raman optical field-excited spin coherence has a frozen propagation vector. Unlike photon echoes whose quantum memory application is strictly limited due to πrephasing pulse-induced population inversion causing quantum noises, the optical Raman field-excited spin echo is inherently silent owing to the frozen propagation vector. Thus, the doubly rephased Raman echo can be directly applied for quantum interface in a population inversion…
I theoretically study the behavior of strong pulses exciting emitters inside a cavity. The ensemble is supposed to be inhomogeneously broadened and the cavity matched finding application in quantum storage of optical or RF photons. My analysis is based on energy and pulse area conservation rules predicting important distortions for specific areas. It is well supported by numerical simulations. I propose a qualitative interpretation in terms of slow-light. The analogy with the free space situation is remarkable.
We demonstrate experimentally a quantum memory scheme for the storage of weak coherent light pulses in an inhomogeneously broadened optical transition in a Pr^{3+}: YSO crystal at 2.1 K. Precise optical pumping using a frequency stable (about 1kHz linewidth) laser is employed to create a highly controllable Atomic Frequency Comb (AFC) structure. We report single photon storage and retrieval efficiencies of 25%, based on coherent photon echo type re-emission in the forward direction. The coherence property of the quantum memory is proved through interference between a super Gaussian pulse and t…
Pulses applied to an inhomogeneously broadened set of harmonic oscillators, previously prepared in squeezed states, can lead to a recovery of coherence, manifesting itself as echoes, similar to those exhibited by an ensemble of spins when excited by properly designed electromagnetic pulses. Such echoes, of classical or quantum nature, are expected to arise in the squeezing of linear systems of various sorts and, in particular, light and vibrational modes.
Inhomogeneously broadened spin ensembles play an important role in present-day implementation of hybrid quantum processing architectures. When coupled to a resonator such an ensemble may serve as a multi-mode quantum memory for the resonator field, and by employing spin-refocusing techniques the quantum memory time can be extended to the coherence time of individual spins in the ensemble. In the present paper we investigate such a memory protocol capable of storing an unknown resonator-field state, and we examine separately the various constituents of the protocol: the storage and read-out par…
We investigate the performance of inhomogeneously broadened spin ensembles as quantum memories under continuous dynamical decoupling. The role of the continuous driving field is two-fold: first, it decouples individual spins from magnetic noise; second and more important, it suppresses and reshapes the spectral inhomogeneity of spin ensembles. We show that a continuous driving field, which itself may also be inhomogeneous over the ensemble, can enhance the decay of the tails of the inhomogeneous broadening distribution considerably. This fact enables a spin ensemble based quantum memory to exp…
Photon-echo based quantum memories use inhomogeneously broadened, optically thick ensembles of absorbers to store a weak optical signal and employ various protocols to rephase the atomic coherences for information retrieval. We study the application of two consecutive, frequency-chirped control pulses for coherence rephasing in an ensemble with a 'natural' inhomogeneous broadening. Although propagation effects distort the two control pulses differently, chirped pulses that drive adiabatic passage can rephase atomic coherences in an optically thick storage medium. Combined with spatial phase mi…
We study the excitation dynamics of an inhomogeneously broadened spin ensemble coupled to a single cavity mode. The collective excitations of the spin ensemble can be described in terms of generalized spin waves and, in the absence of the cavity, the free evolution of the spin ensemble can be described as a drift in the wave number without dispersion. In this article we show that the dynamics in the presence of coupling to the cavity mode can be described solely by a modified time evolution of the wave numbers. In particular, we show that collective excitations with a well- defined wave number…
Photon-echo based optical quantum memory schemes often employ intermediate steps to transform optical coherences to spin coherences for longer storage times. We analyze a scheme that uses three identical chirped control pulses for coherence rephasing in an inhomogeneously broadened ensemble of three-level $Λ$-systems. The pulses induce a cyclic permutation of the atomic populations in the adiabatic regime. Optical coherences created by a signal pulse are stored as spin coherences at an intermediate time interval, and are rephased for echo emission when the ensemble is returned to the initial s…
The three-pulse photon echo is a well-known technique to store intense light pulses in an inhomogeneously broadened atomic ensemble. This protocol is attractive because it is relatively simple and it is well suited for the storage of multiple temporal modes. Furthermore, it offers very long storage times, greater than the phase relaxation time. Here, we consider the three-pulse photon echo in both two- and three-level systems as a potential technique for the storage of light at the single-photon level. By explicit calculations, we show that the ratio between the echo signal corresponding to a …
We demonstrate an all-optical Raman spin echo technique, using Electromagnetically Induced Transparency (EIT) to create the different pulses of the spin echo sequence: initialization, pi-rotation, and readout. The first pulse of the sequence induces coherence directly from a mixed state, and the technique is used to measure the nuclear spin coherence of an inhomogeneously broadened ensemble of rare-earth ions (Pr$^{3+}$). In contrast to previous experiments it does not require any preparatory hole burning pulse sequences, which greatly shortens the total duration of the sequence. The effect of…
We present a light-storage experiment in a praseodymium-doped crystal where the light is mapped onto an inhomogeneously broadened optical transition shaped into an atomic frequency comb. After absorption of the light the optical excitation is converted into a spin-wave excitation by a control pulse. A second control pulse reads the memory (on-demand) by reconverting the spin-wave excitation to an optical one, where the comb structure causes a photon-echo type rephasing of the dipole moments and directional retrieval of the light. This combination of photon echo and spin-wave storage allows us …
Quantum sensing with solid-state systems finds broad applications in diverse areas ranging from material and biomedical sciences to fundamental physics. Several solid-state spin sensors have been developed, facilitating the ultra-sensitive detection of physical quantities such as magnetic and electric fields and temperature. Exploiting collective behaviour of non-interacting spins holds the promise of pushing the detection limit to even lower levels, while to date, those levels are scarcely reached due to the broadened linewidth and inefficient readout of solid-state spin ensembles. Here, we e…
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 effects of dispersion in carrier waves on the properties of soliton self--induced transparency (SIT) in two level media. We found substantial impact of dispersion effects on typical SIT soliton features. For example, the degree of SIT pulse velocity slowing down (acceleration) is determined by the ratio of the incoming pulse frequency over atomic transition frequency - $x=ω/ω_0$. Specifically, an immediate pulse stopping is predicted for absorbing media when pulse duration time exceeds some critical value. In the sharp line limit stopping may emerge only for frequency ratio above …
We present a theoretical study on the nonlinear dynamics and stationary states of an inhomogeneously broadened spin ensemble coupled to a single-mode cavity driven by an external drive with constant amplitude. Assuming a sizeable number of constituents within the ensemble allows us to use a semiclassical approach and to formally reduce the theoretical description to the Maxwell-Bloch equations for the cavity and spin amplitudes. We explore the critical slowing-down effect, quench dynamics, and asymptotic behavior of the system near a steady-state dissipative phase transition accompanied by a b…
Ensembles of electron spins in hybrid microwave systems are powerful and versatile components for future quantum technologies. Quantum memories with high storage capacities are one such example which require long-lived states that can be addressed and manipulated coherently within the inhomogeneously broadened ensemble. This broadening is essential for true multimode memories, but induces a considerable spin dephasing and together with dissipation from a cavity interface poses a constraint on the memory's storage time. In this work we show how to overcome both of these limitations through the …
