Individual Two-level Systems Research Articles

Two-photon pumped exciton-polariton condensation

Two-photon absorption (TPA) allows accessing “dark” states of matter that are otherwise inaccessible to light, which serve as important building blocks for quantum information processing. In a semiconductor microcavity, TPA-driven condensation of strongly coupled light-matter exciton–polaritons can enable new solid-state quantum simulations of “dark” state-condensate interactions and was predicted to stimulate THz emission. Here, we report the first observation of two-photon-pumped polariton condensation, demonstrated by angle-resolved photoluminescence in a GaAs-based microcavity. TPA is evidenced in the quadratic emission dependence on pump power below and above the condensation threshold, and second-harmonic generation is ruled out by both this threshold behavior and by the emission peak energy showing no dependence on pump photon energy. Our results pave the way toward novel polariton-based sources and solid-state coherent control of collective quantum states with individual two-level systems.

Quantum state interrogation using a preshaped free electron wavefunction

We present a comprehensive theory for interrogation of the quantum state of a two-level system (TLS) based on a free-electron--bound-electron resonant interaction scheme. The scheme is based on free electrons, whose quantum electron wavefunction is preshaped or optically modulated by lasers in an electron microscope setup and then inelastically scattered by a quantum TLS target (e.g., atom, quantum dot, and crystal defect center) upon traversing in proximity to the target. Measurement of the postinteraction energy spectrum of the electrons probes and quantifies the full Bloch sphere parameters of a pre-excited TLS and enables coherent control of the qubit states. The exceptional advantage of this scheme over laser-based ones is atomic-scale spatial resolution of addressing individual TLS targets. Thus, this scheme opens horizons for electron microscopy in material interrogation and quantum information technology.

Probing the Tavis-Cummings Level Splitting with Intermediate-Scale Superconducting Circuits

We demonstrate the local control of up to eight two-level systems interacting strongly with a microwave cavity. Following calibration, the frequency of each individual two-level system (qubit) is tunable without influencing the others. Bringing the qubits one by one on resonance with the cavity, we observe the collective coupling strength of the qubit ensemble. The splitting scales up with the square root of the number of the qubits, which is the hallmark of the Tavis-Cummings model. The local control circuitry causes a bypass shunting the resonator, and a Fano interference in the microwave readout, whose contribution can be calibrated away to recover the pure cavity spectrum. The simulator's attainable size of dressed states with up to five qubits is limited by reduced signal visibility, and -- if uncalibrated -- by off-resonance shifts of sub-components. Our work demonstrates control and readout of quantum coherent mesoscopic multi-qubit system of intermediate scale under conditions of noise.

Measurement Induced Synthesis of Coherent Quantum Batteries

Quantum coherence represented by a superposition of energy eigenstates is, together with energy, an important resource for quantum technology and thermodynamics. Energy and quantum coherence however, can be complementary. The increase of energy can reduce quantum coherence and vice versa. Recently, it was realized that steady-state quantum coherence could be autonomously harnessed from a cold environment. We propose a conditional synthesis of N independent two-level systems (TLS) with partial quantum coherence obtained from an environment to one coherent system using a measurement able to increase both energy and coherence simultaneously. The measurement process acts here as a Maxwell demon synthesizing the coherent energy of individual TLS to one large coherent quantum battery. The measurement process described by POVM elements is diagonal in energy representation and, therefore, it does not project on states with quantum coherence at all. We discuss various strategies and their efficiency to reach large coherent energy of the battery. After numerical optimization and proof-of-principle tests, it opens way to feasible repeat-until-success synthesis of coherent quantum batteries from steady-state autonomous coherence.

Decoherence benchmarking of superconducting qubits

We benchmark the decoherence of superconducting transmon qubits to examine the temporal stability of energy relaxation, dephasing, and qubit transition frequency. By collecting statistics during measurements spanning multiple days, we find the mean parameters overline {T_1} = 49 μs and overline {T_2^ ast } = 95 μs; however, both of these quantities fluctuate, explaining the need for frequent re-calibration in qubit setups. Our main finding is that fluctuations in qubit relaxation are local to the qubit and are caused by instabilities of near-resonant two-level-systems (TLS). Through statistical analysis, we determine sub-millihertz switching rates of these TLS and observe the coherent coupling between an individual TLS and a transmon qubit. Finally, we find evidence that the qubit’s frequency stability produces a 0.8 ms limit on the pure dephasing which we also observe. These findings raise the need for performing qubit metrology to examine the reproducibility of qubit parameters, where these fluctuations could affect qubit gate fidelity.

Free-Space Quantum Electrodynamics with a Single Rydberg Superatom

The interaction of a single photon with an individual two-level system is the textbook example of quantum electrodynamics. Achieving strong coupling in this system so far required confinement of the light field inside resonators or waveguides. Here, we demonstrate strong coherent coupling between a single Rydberg superatom, consisting of thousands of atoms behaving as a single two-level system due to the Rydberg blockade, and a propagating light pulse containing only a few photons. The strong light-matter coupling in combination with the direct access to the outgoing field allows us to observe for the first time the effect of the interactions on the driving field at the single photon level. We find that all our results are in quantitative agreement with the predictions of the theory of a single two-level system strongly coupled to a single quantized propagating light mode. The demonstrated coupling strength opens the way towards interfacing photonic and atomic qubits and preparation of propagating non-classical states of light, two crucial building blocks in future quantum networks.

Electronic decoherence of two-level systems in a Josephson junction

The sensitivity of superconducting qubits allows for spectroscopy and coherence measurements on individual two-level systems present in the disordered tunnel barrier of an $\mathrm{Al/AlO_x/Al}$ Josephson junction. We report experimental evidence for the decoherence of two-level systems by Bogoliubov quasiparticles leaking into the insulating $\mathrm{AlO_x}$ barrier. We control the density of quasiparticles in the junction electrodes either by the sample temperature or by injecting them using an on-chip dc-SQUID driven to its resistive state. The decoherence rates were measured by observing the two-level system's quantum state evolving under application of resonant microwave pulses and were found to increase linearly with quasiparticle density, in agreement with theory. This interaction with electronic states provides a noise and decoherence mechanism that is relevant for various microfabricated devices such as qubits, single-electron transistors, and field-effect transistors. The presented experiments also offer a possibility to determine the location of the probed two-level systems across the tunnel barrier, providing clues about the fabrication step in which they emerge.

Revealing the nonlinear response of a tunneling two-level system ensemble using coupled modes

Atomic sized two-level systems (TLSs) in amorphous dielectrics are known as a major source of loss in superconducting devices. In addition, individual TLS are known to induce large frequency shifts due to strong coupling to the devices. However, in the presence of a broad ensemble of TLSs these shifts are symmetrically canceled out and not observed in a typical single-tone spectroscopy experiment. We introduce a two-tone spectroscopy on the normal modes of a pair of coupled superconducting coplanar waveguide resonators to reveal this effect. Together with an appropriate saturation model this enables us to extract the average single-photon Rabi frequency of dominant TLSs to be $\Omega_0/2\pi \approx 79 $ kHz. At high photon numbers we observe an enhanced frequency shift due to nonlinear kinetic inductance when using the two-tone method and estimate the value of the nonlinear coefficient as $K/2\pi \approx -1\times 10^{-4}$ Hz/photon. Furthermore, the life-time of each resonance can be controlled (increased) by pumping of the other mode as demonstrated both experimentally and theoretically.

Molecular spectra in collective Dicke states

We study a model describing competition of interactions between $N$ two-level systems (TLSs) against decoherence. We apply it to analyze dye molecules in an optical microcavity, where molecular vibrations provide a local source for decoherence. Most interesting is the case when decoherence strongly affects each individual TLS, e.g. via broadening of emission lines as well as vibrational satellites, however its influence is strongly suppressed for large $N$ due to the interactions between TLSs. In this interaction dominated regime we find unique signatures in the emission spectrum, including strong $\mathcal{O}(\sqrt{N})$ level shifts, as well as $1/N$ suppression of both the decoherence width and of the vibrational satellites.

Multi-wave coherent control of a solid-state single emitter

Coherent control of individual two-level systems (TLSs) is at the basis of any implementation of quantum information. An impressive level of control is now achieved using nuclear, vacancies and charge spins. Manipulation of bright exciton transitions in semiconductor quantum dots (QDs) is less advanced, principally due to the sub-nanosecond dephasing. Conversely, owing to their robust coupling to light, one can apply tools of nonlinear spectroscopy to achieve all-optical command. Here, we report on the coherent manipulation of an exciton via multi-wave mixing. Specifically, we employ three resonant pulses driving a single InAs QD. The first two induce a four-wave mixing (FWM) transient, which is projected onto a six-wave mixing (SWM) depending on the delay and area of the third pulse, in agreement with analytical predictions. Such a switch enables to demonstrate the generation of SWM on a single emitter and to engineer the spectro-temporal shape of the coherent response originating from a TLS. These results pave the way toward multi-pulse manipulations of solid state qubits via implementing the NMR-like control schemes in the optical domain.

Single quantum dot controls a plasmonic cavity’s scattering and anisotropy

Plasmonic cavities represent a promising platform for controlling light-matter interaction due to their exceptionally small mode volume and high density of photonic states. Using plasmonic cavities for enhancing light's coupling to individual two-level systems, such as single semiconductor quantum dots (QD), is particularly desirable for exploring cavity quantum electrodynamic (QED) effects and using them in quantum information applications. The lack of experimental progress in this area is in part due to the difficulty of precisely placing a QD within nanometers of the plasmonic cavity. Here, we study the simplest plasmonic cavity in the form of a spherical metallic nanoparticle (MNP). By controllably positioning a semiconductor QD in the close proximity of the MNP cavity via atomic force microscope (AFM) manipulation, the scattering spectrum of the MNP is dramatically modified due to Fano interference between the classical plasmonic resonance of the MNP and the quantized exciton resonance in the QD. Moreover, our experiment demonstrates that a single two-level system can render a spherical MNP strongly anisotropic. These findings represent an important step toward realizing quantum plasmonic devices.

Robust quantum storage and retrieval in a hybrid system by controllable Stark-chirped rapid adiabatic passages

Quantum memory is one of the basic building blocks in large-scale quantum computers. In the paper, we propose a scheme to realize a quantum memory in a hybrid system by controllable Stark-chirped rapid adiabatic passages. In the hybrid system, by taking advantage of long coherence times in microscopic system, which is a two-level system naturally embedded in a current-biased Josephson junction, individual two-level system can be regarded as a quantum memory. The scheme of storage and retrieval is realized by Stark-chirped rapid adiabatic passages, which is insensitive to the details of the applied adiabatic pulses. In numerical investigation of the storage process using adiabatic master equations, we demonstrate that high-fidelity quantum memory can be achieved under practical noises. Finally, the experimental feasibility and performance are discussed based on the current experimental status.

Realizing Strong Light-Matter Interactions between Single-Nanoparticle Plasmons and Molecular Excitons at Ambient Conditions.

Realizing strong light-matter interactions between individual two-level systems and resonating cavities in atomic and solid state systems opens up possibilities to study optical nonlinearities on a single-photon level, which can be useful for future quantum information processing networks. However, these efforts have been hampered by unfavorable experimental conditions, such as cryogenic temperatures and ultrahigh vacuum, required to study such systems and phenomena. Although several attempts to realize strong light-matter interactions at room temperature using plasmon resonances have been made, successful realizations on the single-nanoparticle level are still lacking. Here, we demonstrate the strong coupling between plasmons confined within a single silver nanoprism and excitons in molecular J aggregates at ambient conditions. Our findings show that deep subwavelength mode volumes V together with quality factors Q that are reasonably high for plasmonic nanostructures result in a strong-coupling figure of merit-Q/sqrt[V] as high as ∼6×10^{3} μm^{-3/2}, a value comparable to state-of-the-art photonic crystal and microring resonator cavities. This suggests that plasmonic nanocavities, and specifically silver nanoprisms, can be used for room temperature quantum optics.

Quantum superposition of localized and delocalized phases of photons

Based on a variant of 2-site Jaynes–Cummings–Hubbard model constructed using superconducting circuits, we propose a method to coherently superpose the localized and delocalized phases of microwave photons, which makes it possible to engineer the collective features of multiple photons in the quantum way using an individual two-level system. Our proposed architecture is also a promising candidate for implementing distributed quantum computation since it is capable of coupling remote qubits in separate resonators in a controllable way.

Measuring the Temperature Dependence of Individual Two-Level Systems by Direct Coherent Control

We demonstrate a new method to directly manipulate the state of individual two-level systems (TLSs) in phase qubits. It allows one to characterize the coherence properties of TLSs using standard microwave pulse sequences, while the qubit is used only for state readout. We apply this method to measure the temperature dependence of TLS coherence for the first time. The energy relaxation time T1 is found to decrease quadratically with temperature for the two TLSs studied in this work, while their dephasing time measured in Ramsey and spin-echo experiments is found to be T1 limited at all temperatures.

Control and imaging of single-molecule spectral dynamics using a nano-electrode

We study the influence of a scanning nano-electrode on the fluorescence excitation spectra of single terrylene molecules embedded in thin p-terphenyl films at cryogenic temperatures. We show that applied voltages of less than 10 V can result in reversible Stark shifts of up to 100 times and a linewidth increase greater than 10 times the natural linewidth. We discuss the potential of our experimental scheme for the direct imaging of individual two-level systems in the nanometer vicinity of single molecules.

Strong coupling in a single quantum dot–semiconductor microcavity system

Cavity quantum electrodynamics, a central research field in optics and solid-state physics, addresses properties of atom-like emitters in cavities and can be divided into a weak and a strong coupling regime. For weak coupling, the spontaneous emission can be enhanced or reduced compared with its vacuum level by tuning discrete cavity modes in and out of resonance with the emitter. However, the most striking change of emission properties occurs when the conditions for strong coupling are fulfilled. In this case there is a change from the usual irreversible spontaneous emission to a reversible exchange of energy between the emitter and the cavity mode. This coherent coupling may provide a basis for future applications in quantum information processing or schemes for coherent control. Until now, strong coupling of individual two-level systems has been observed only for atoms in large cavities. Here we report the observation of strong coupling of a single two-level solid-state system with a photon, as realized by a single quantum dot in a semiconductor microcavity. The strong coupling is manifest in photoluminescence data that display anti-crossings between the quantum dot exciton and cavity-mode dispersion relations, characterized by a vacuum Rabi splitting of about 140 microeV.

Phase-dependent fluorescence linewidth narrowing in a three-level atom damped by a finite-bandwidth squeezed vacuum

We examine subnatural phase-dependent linewidths in the fluorescence spectrum of a three-level atom damped by a narrow-bandwidth squeezed vacuum in a cavity. Using the dressed-atom model approach of a strongly driven three-level cascade system, we derive the master equation of the system from which we obtain simple analytical expressions for the fluorescence spectrum. We show that the phase effects depend on the bandwidths of the squeezed vacuum and the cavity relative to the Rabi frequency of the driving fields. When the squeezing bandwidth is much larger than the Rabi frequency, the spectrum consists of five lines with only the central and outer sidebands dependent on the phase. For a squeezing bandwidth much smaller than the Rabi frequency the number of lines in the spectrum and their phase properties depend on the frequency at which the squeezing and cavity modes are centered. When the squeezing and cavity modes are centered on the inner Rabi sidebands, the spectrum exhibits five lines that are completely independent of the squeezing phase with only the inner Rabi sidebands dependent on the squeezing correlations. Matching the squeezing and cavity modes to the outer Rabi sidebands leads to the disappearance of the inner Rabi sidebands and a strong phase dependence of the central line and the outer Rabi sidebands. We find that in this case the system behaves as an individual two-level system that reveals exactly the noise distribution in the input squeezed vacuum.

Spectral diffusion and individual two-level systems probed by fluorescence of single terrylene molecules in a polyethylene matrix

We study the influence of low-energy matrix excitations on the line widths and fluorescence correlation of single terrylene molecules in polyethylene at helium temperatures. The histogram of line widths has a cutoff at the natural line width of terrylene, showing that for some molecules dephasing and spectral diffusion are negligible on the measurement time scale. The shape of the histogram can be qualitatively interpreted by means of a simple model for spectral diffusion. The line widths of different molecules show different temperature dependences. The correlation method is then applied to a time-resolved study of the intensity fluctuations of single molecule fluorescence. Many possible shapes of correlation functions appear, spanning many decades of relaxation times. We believe single two-level systems (TLSs) are the cause of the well defined exponential steps we observe. In some cases, the two positions of a single molecule's line can be identified in the spectrum. They present the same time constant in their correlation functions and jump together to a new frequency. The dependence of the correlation on exciting flux shows that jumps can be spontaneous or photo-induced. The study of the rate as a function of temperature shows clear power laws which we attribute to tunnelling of the TLS assisted by one ( T 1) or two ( T 3) acoustic phonons. In one case, we find an Arrhenius activation of the rate, which could be explained by dressing the standard TLS model with slow matrix modes.

Probing individual two-level systems in a polymer by correlation of single molecule fluorescence.

We have measured the autocorrelation of the fluorescence of single aromatic molecules in polyethylene at T\ensuremath{\approxeq}2 K. Assuming intensity fluctuations to be caused by frequency jumps when two-level systems (TLS's) change states, we show that individual TLS's can be probed, allowing direct measurement of some of their properties, with minimal recourse to theory and no assumptions about the distribution of TLS parameters. Besides providing a simple confirmation of the tunneling theory of TLS's, this new method, by eliminating statistical uncertainties, proves that while some TLS's may be stable for several hours others are modified by transitions of their neighbors. Tunneling times of individual TLS's are measured directly, as are their temperature dependences, revealing three types of TLS-phonon coupling, of which one is new.