Efficient multimode Wigner tomography

Advancements in quantum system lifetimes and control have enabled the creation of increasingly complex quantum states, such as those on multiple bosonic cavity modes. When characterizing these states, traditional tomography scales exponentially with the number of modes in both computational and experimental measurement requirement, which becomes prohibitive as the system size increases. Here, we implement a state reconstruction method whose sampling requirement instead scales polynomially with system size, and thus mode number, for states that can be represented within such a polynomial subspace. We demonstrate this improved scaling with Wigner tomography of multimode entangled W states of up to 4 modes on a 3D circuit quantum electrodynamics (cQED) system. This approach performs similarly in efficiency to existing matrix inversion methods for 2 modes, and demonstrates a noticeable improvement for 3 and 4 modes, with even greater theoretical gains at higher mode numbers.

Stimulated Emission of Signal Photons from Dark Matter Waves

The manipulation of quantum states of light has resulted in significant advancements in both dark matter searches and gravitational wave detectors. Current dark matter searches operating in the microwave frequency range use nearly quantum-limited amplifiers. Future high frequency searches will use photon counting techniques to evade the standard quantum limit. We present a signal enhancement technique that utilizes a superconducting qubit to prepare a superconducting microwave cavity in a nonclassical Fock state and stimulate the emission of a photon from a dark matter wave. By initializing the cavity in an |n=4⟩ Fock state, we demonstrate a quantum enhancement technique that increases the signal photon rate and hence also the dark matter scan rate each by a factor of 2.78. Using this technique, we conduct a dark photon search in a band around 5.965 GHz (24.67  μeV), where the kinetic mixing angle ε≥4.35×10^{-13} is excluded at the 90% confidence level.

Autonomous error correction of a single logical qubit using two transmons

Large-scale quantum computers will inevitably need quantum error correction to protect information against decoherence. Traditional error correction typically requires many qubits, along with high-efficiency error syndrome measurement and real-time feedback. Autonomous quantum error correction instead uses steady-state bath engineering to perform the correction in a hardware-efficient manner. In this work, we develop a new autonomous quantum error correction scheme that actively corrects single-photon loss and passively suppresses low-frequency dephasing, and we demonstrate an important experimental step towards its full implementation with transmons. Compared to uncorrected encoding, improvements are experimentally witnessed for the logical zero, one, and superposition states. Our results show the potential of implementing hardware-efficient autonomous quantum error correction to enhance the reliability of a transmon-based quantum information processor.

Quantum-enabled millimetre wave to optical transduction using neutral atoms

Early experiments with transiting circular Rydberg atoms in a superconducting resonator laid the foundations of modern cavity and circuit quantum electrodynamics1, and helped explore the defining features of quantum mechanics such as entanglement. Whereas ultracold atoms and superconducting circuits have since taken rather independent paths in the exploration of new physics, taking advantage of their complementary strengths in an integrated system enables access to fundamentally new parameter regimes and device capabilities2,3. Here we report on such a system, coupling an ensemble of cold 85Rb atoms simultaneously to an, as far as we are aware, first-of-its-kind optically accessible, three-dimensional superconducting resonator4 and a vibration-suppressed optical cavity in a cryogenic (5 K) environment. To demonstrate the capabilities of this platform, and with an eye towards quantum networking5, we leverage the strong coupling between Rydberg atoms and the superconducting resonator to implement a quantum-enabled millimetre wave (mmwave) photon to optical photon transducer6. We measured an internal conversion efficiency of 58(11)%, a conversion bandwidth of 360(20) kHz and added thermal noise of 0.6 photons, in agreement with a parameter-free theory. Extensions of this technique will allow near-unity efficiency transduction in both the mmwave and microwave regimes. More broadly, our results open a new field of hybrid mmwave/optical quantum science, with prospects for operation deep in the strong coupling regime for efficient generation of metrologically or computationally useful entangled states7 and quantum simulation/computation with strong non-local interactions8.

The QICK (Quantum Instrumentation Control Kit): Readout and control for qubits and detectors

We introduce a Xilinx RF System-on-Chip (RFSoC)-based qubit controller (called the Quantum Instrumentation Control Kit, or QICK for short), which supports the direct synthesis of control pulses with carrier frequencies of up to 6 GHz. The QICK can control multiple qubits or other quantum devices. The QICK consists of a digital board hosting an RFSoC field-programmable gate array, custom firmware, and software and an optional companion custom-designed analog front-end board. We characterize the analog performance of the system as well as its digital latency, important for quantum error correction and feedback protocols. We benchmark the controller by performing standard characterizations of a transmon qubit. We achieve an average gate fidelity of F_avg=99.93%. All of the schematics, firmware, and software are open-source.

Seamless High-Q Microwave Cavities for Multimode Circuit Quantum Electrodynamics

Multimode cavity quantum electrodynamics-where a two-level system interacts simultaneously with many cavity modes-provides a versatile framework for quantum information processing and quantum optics. Because of the combination of long coherence times and large interaction strengths, one of the leading experimental platforms for cavity QED involves coupling a superconducting circuit to a 3D microwave cavity. In this work, we realize a 3D multimode circuit QED system with single photon lifetimes of 2 ms across 9 modes of a novel seamless cavity. We demonstrate a variety of protocols for universal single-mode quantum control applicable across all cavity modes, using only a single drive line. We achieve this by developing a straightforward flute method for creating monolithic superconducting microwave cavities that reduces loss while simultaneously allowing control of the mode spectrum and mode-qubit interaction. We highlight the flexibility and ease of implementation of this technique by using it to fabricate a variety of 3D cavity geometries, providing a template for engineering multimode quantum systems with exceptionally low dissipation. This work is an important step towards realizing hardware efficient random access quantum memories and processors, and for exploring quantum many-body physics with photons.

Searching for Dark Matter with a Superconducting Qubit

Detection mechanisms for low mass bosonic dark matter candidates, such as the axion or hidden photon, leverage potential interactions with electromagnetic fields, whereby the dark matter (of unknown mass) on rare occasion converts into a single photon. Current dark matter searches operating at microwave frequencies use a resonant cavity to coherently accumulate the field sourced by the dark matter and a near standard quantum limited (SQL) linear amplifier to read out the cavity signal. To further increase sensitivity to the dark matter signal, sub-SQL detection techniques are required. Here we report the development of a novel microwave photon counting technique and a new exclusion limit on hidden photon dark matter. We operate a superconducting qubit to make repeated quantum nondemolition measurements of cavity photons and apply a hidden Markov model analysis to reduce the noise to 15.7 dB below the quantum limit, with overall detector performance limited by a residual background of real photons. With the present device, we perform a hidden photon search and constrain the kinetic mixing angle to ε≤1.68×10^{-15} in a band around 6.011 GHz (24.86  μeV) with an integration time of 8.33 s. This demonstrated noise reduction technique enables future dark matter searches to be sped up by a factor of 1,300. By coupling a qubit to an arbitrary quantum sensor, more general sub-SQL metrology is possible with the techniques presented in this Letter.

Deterministic multi-qubit entanglement in a quantum network

The generation of high-fidelity distributed multi-qubit entanglement is a challenging task for large-scale quantum communication and computational networks^1-4. The deterministic entanglement of two remote qubits has recently been demonstrated with both photons^5-10 and phonons¹¹. However, the deterministic generation and transmission of multi-qubit entanglement has not been demonstrated, primarily owing to limited state-transfer fidelities. Here we report a quantum network comprising two superconducting quantum nodes connected by a one-metre-long superconducting coaxial cable, where each node includes three interconnected qubits. By directly connecting the cable to one qubit in each node, we transfer quantum states between the nodes with a process fidelity of 0.911 ± 0.008. We also prepare a three-qubit Greenberger-Horne-Zeilinger (GHZ) state^12-14 in one node and deterministically transfer this state to the other node, with a transferred-state fidelity of 0.656 ± 0.014. We further use this system to deterministically generate a globally distributed two-node, six-qubit GHZ state with a state fidelity of 0.722 ± 0.021. The GHZ state fidelities are clearly above the threshold of 1/2 for genuine multipartite entanglement¹⁵, showing that this architecture can be used to coherently link together multiple superconducting quantum processors, providing a modular approach for building large-scale quantum computers^16,17.

Optical mode conversion in coupled Fabry-Perot resonators

Low-loss conversion among a complete and orthogonal set of optical modes is important for high-bandwidth quantum and classical communication. In this Letter, we explore tunable impedance mismatch between coupled Fabry-Perot resonators as a powerful tool for manipulation of the spatial and temporal properties of optical fields. In the single-mode regime, frequency-dependent impedance matching enables tunable finesse optical resonators. Introducing the spatial dependence of the impedance mismatch enables coherent spatial mode conversion of optical photons at near-unity efficiency. We experimentally demonstrate a NIR resonator whose finesse is tunable over a decade, and an optical mode converter with efficiency >75% for the first six Hermite-Gauss modes. We anticipate that this new perspective on coupled multimode resonators will have exciting applications in micro- and nano-photonics and computer-aided inverse design.

Design, synthesis and photoinduced processes in molecular interlocked photosynthetic [60]fullerene systems

The mechanical bond, an entanglement in space between component parts that cannot be separated without breaking or distorting chemical bonds between atoms, can be used as a versatile organizing principle in the design of artificial photosynthetic systems.

Two-Dimensional Material Tunnel Barrier for Josephson Junctions and Superconducting Qubits

Quantum computing based on superconducting qubits requires the understanding and control of the materials, device architecture, and operation. However, the materials for the central circuit element, the Josephson junction, have mostly been focused on using the AlO_x tunnel barrier. Here, we demonstrate Josephson junctions and superconducting qubits employing two-dimensional materials as the tunnel barrier. We batch-fabricate and design the critical Josephson current of these devices via layer-by-layer stacking N layers of MoS₂ on the large scale. Based on such junctions, MoS₂ transmon qubits are engineered and characterized in a bulk superconducting microwave resonator for the first time. Our work allows Josephson junctions to access the diverse material properties of two-dimensional materials that include a wide range of electrical and magnetic properties, which can be used to study the effects of different material properties in superconducting qubits and to engineer novel quantum circuit elements in the future.

Author Correction: A dissipatively stabilized Mott insulator of photons

Change history: In this Article, two additional references (now added as refs ¹² and ¹⁴) should have been cited at the end of the sentence "Recently, photonic systems have emerged as a platform of interest for the exploration of synthetic quantum matter.". This has been corrected online.

Realization of a Λ System with Metastable States of a Capacitively Shunted Fluxonium

We realize a Λ system in a superconducting circuit, with metastable states exhibiting lifetimes up to 8 ms. We exponentially suppress the tunneling matrix elements involved in spontaneous energy relaxation by creating a "heavy" fluxonium, realized by adding a capacitive shunt to the original circuit design. The device allows for both cavity-assisted and direct fluorescent readouts, as well as state preparation schemes akin to optical pumping. Since direct transitions between the metastable states are strongly suppressed, we utilize Raman transitions for coherent manipulation of the states.

Publisher Correction: Random access quantum information processors using multimode circuit quantum electrodynamics

In the original version of this Article, the affiliation details for Peter Groszkowski and Jens Koch were incorrectly given as 'Department of Physics, University of Chicago, Chicago, IL, 60637, USA', instead of the correct 'Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA'. This has now been corrected in both the PDF and HTML versions of the Article.

Understanding Quality Factor Degradation in Superconducting Niobium Cavities at Low Microwave Field Amplitudes

In niobium superconducting radio frequency (SRF) cavities for particle acceleration, a decrease of the quality factor at lower fields-a so-called low field Q slope or LFQS-has been a long-standing unexplained effect. By extending the high Q measurement techniques to ultralow fields, we discover two previously unknown features of the effect: (i) saturation at rf fields lower than E_{acc}∼0.1  MV/m; (ii) strong degradation enhancement by growing thicker niobium pentoxide. Our findings suggest that the LFQS may be caused by the two level systems in the natural niobium oxide on the inner cavity surface, thereby identifying a new source of residual resistance and providing guidance for potential nonaccelerator low-field applications of SRF cavities.

Random access quantum information processors using multimode circuit quantum electrodynamics

Qubit connectivity is an important property of a quantum processor, with an ideal processor having random access—the ability of arbitrary qubit pairs to interact directly. This a challenge with superconducting circuits, as state-of-the-art architectures rely on only nearest-neighbor coupling. Here, we implement a random access superconducting quantum information processor, demonstrating universal operations on a nine-qubit memory, with a Josephson junction transmon circuit serving as the central processor. The quantum memory uses the eigenmodes of a linear array of coupled superconducting resonators. We selectively stimulate vacuum Rabi oscillations between the transmon and individual eigenmodes through parametric flux modulation of the transmon frequency. Utilizing these oscillations, we perform a universal set of quantum gates on 38 arbitrary pairs of modes and prepare multimode entangled states, all using only two control lines. We thus achieve hardware-efficient random access multi-qubit control in an architecture compatible with long-lived microwave cavity-based quantum memories.

Despite their versatility, superconducting qubits such as transmons still have limited coherence times compared to resonators. Here, the authors show how to use a single transmon to implement universal one-qubit and two-qubit operations among nine qubits encoded in superconducting resonators’ eigenmodes.

Universal Stabilization of a Parametrically Coupled Qubit

We autonomously stabilize arbitrary states of a qubit through parametric modulation of the coupling between a fixed frequency qubit and resonator. The coupling modulation is achieved with a tunable coupling design, in which the qubit and the resonator are connected in parallel to a superconducting quantum interference device. This allows for quasistatic tuning of the qubit-cavity coupling strength from 12 MHz to more than 300 MHz. Additionally, the coupling can be dynamically modulated, allowing for single-photon exchange in 6 ns. Qubit coherence times exceeding 20  μs are maintained over the majority of the range of tuning, limited primarily by the Purcell effect. The parametric stabilization technique realized using the tunable coupler involves engineering the qubit bath through a combination of photon nonconserving sideband interactions realized by flux modulation, and direct qubit Rabi driving. We demonstrate that the qubit can be stabilized to arbitrary states on the Bloch sphere with a worst-case fidelity exceeding 80%.

John D. Roberts (1918-2016)

John D. (Jack) Roberts, Institute Professor of Chemistry Emeritus at the California Institute of Technology died on October 29, 2016, at the age of 98. Roberts was one of the of the iconic figures in physical organic chemistry of the 20th century. His achievements included proving the occurrence of benzynes and nonclassical carbocations as reaction intermediates, and he was instrumental in establishing NMR spectroscopy as a standard analytical technique in organic chemistry.

Multistep energy and electron transfer processes in novel rotaxane donor-acceptor hybrids generating microsecond-lived charge separated states

A new set of [Cu(phen)2]+ based rotaxanes, featuring [60]-fullerene as an electron acceptor and a variety of electron donating moieties, namely zinc porphyrin (ZnP), zinc phthalocyanine (ZnPc) and ferrocene (Fc), has been synthesized and fully characterized with respect to electrochemical and photophysical properties. The assembly of the rotaxanes has been achieved using a slight variation of our previously reported synthetic strategy that combines the Cu(i)-catalyzed azide-alkyne cycloaddition reaction (the "click" or CuAAC reaction) with Sauvage's metal-template protocol. To underline our results, complementary model rotaxanes and catenanes have been prepared using the same strategy and their electrochemistry and photo-induced processes have been investigated. Insights into excited state interactions have been afforded from steady state and time resolved emission spectroscopy as well as transient absorption spectroscopy. It has been found that photo-excitation of the present rotaxanes triggers a cascade of multi-step energy and electron transfer events that ultimately leads to remarkably long-lived charge separated states featuring one-electron reduced C60 radical anion (C60˙-) and either one-electron oxidized porphyrin (ZnP˙+) or one-electron oxidized ferrocene (Fc˙+) with lifetimes up to 61 microseconds. In addition, shorter-lived charge separated states involving one-electron oxidized copper complexes ([Cu(phen)2]2+ (τ < 100 ns)), one-electron oxidized zinc phthalocyanine (ZnPc˙+; τ = 380-560 ns), or ZnP˙+ (τ = 2.3-8.4 μs), and C60˙- have been identified as intermediates during the sequence. Detailed energy diagrams illustrate the sequence and rate constants of the photophysical events occurring with the mechanically-linked chromophores. This work pioneers the exploration of mechanically-linked systems as platforms to position three distinct chromophores, which are able to absorb light over a very wide range of the visible region, triggering a cascade of short-range energy and electron transfer processes to afford long-lived charge separated states.

High-contrast qubit interactions using multimode cavity QED

We introduce a new multimode cavity QED architecture for superconducting circuits that can be used to implement photonic memories, more efficient Purcell filters, and quantum simulations of photonic materials. We show that qubit interactions mediated by multimode cavities can have exponentially improved contrast for two qubit gates without sacrificing gate speed. Using two qubits coupled via a three-mode cavity system we spectroscopically observe multimode strong couplings up to 102 MHz and demonstrate suppressed interactions off resonance of 10 kHz when the qubits are ≈600  MHz detuned from the cavity resonance. We study Landau-Zener transitions in our multimode systems and demonstrate quasiadiabatic loading of single photons into the multimode cavity in 25 ns. We introduce an adiabatic gate protocol to realize a controlled-Z gate between the qubits in 95 ns and create a Bell state with 94.7% fidelity. This corresponds to an on/off ratio (gate contrast) of 1000.

Synthesis and photophysical properties of new catenated electron donor-acceptor materials with magnesium and free base porphyrins as donors and C60 as the acceptor

A new series of nanoscale electron donor-acceptor systems with [2]catenane architectures has been synthesized, incorporating magnesium porphyrin (MgP) or free base porphyrin (H2P) as electron donor and C60 as electron acceptor, surrounding a central tetrahedral Cu(I)-1,10-phenanthroline (phen) complex. Model catenated compounds incorporating only one or none of these photoactive moieties were also prepared. The synthesis involved the use of Sauvage's metal template protocol in combination with the 1,3-dipolar cycloaddition of azides and alkynes ("click chemistry"), as in other recent reports from our laboratories. Ground state electron interactions between the individual constituents was probed using electrochemistry and UV-vis absorption spectroscopy, while events occurring following photoexcitation in tetrahydrofuran (under both aerobic and anaerobic conditions) at various wavelengths were followed by means of time-resolved transient absorption and emission spectroscopies on the femtosecond and nanosecond time scales, respectively, complemented by measurements of quantum yields for generation of singlet oxygen. From similar studies with model catenates containing one or neither of the chromophores, the events following photoexcitation could be elucidated. The results were compared with those previously reported for analogous catenates based on zinc porphyrin (ZnP). It was determined that a series of energy transfer (EnT) and electron transfer (ET) processes take place in the present catenates, ultimately generating long-distance charge separated (CS) states involving oxidized porphyrin and reduced C60 moieties, with lifetimes ranging from 400 to 1060 nanoseconds. Shorter lived short-distance CS states possessing oxidized copper complexes and reduced C60, with lifetimes ranging from 15 to 60 ns, were formed en route to the long-distance CS states. The dynamics of the ET processes were analyzed in terms of their thermodynamic driving forces. It was clear that intramolecular back ET was occurring in the inverted region of the Marcus parabola correlating rates and driving forces for electron transfer processes. In addition, evidence for triplet excited states as a product of either incomplete ET or back ET was found. The differences in behavior of the three catenates upon photoexcitation are analyzed in terms of the energy levels of the various intermediate states and the driving forces for EnT and ET processes.

Superconducting coplanar waveguide resonators for low temperature pulsed electron spin resonance spectroscopy

We discuss the design and implementation of thin film superconducting coplanar waveguide micro-resonators for pulsed electron spin resonance experiments. The performance of the resonators with P doped Si epilayer samples is compared to waveguide resonators under equivalent conditions. The high achievable filling factor even for small sized samples and the relatively high Q-factor result in a sensitivity of 4.5 × 10(8) spins per shot, which is superior to that of conventional waveguide resonators, in particular to spins close to the sample surface. The peak microwave power is on the order of a few milliwatts, which is compatible with measurements at ultra-low temperatures. We also discuss the effect of the nonuniform microwave magnetic field on the Hahn echo power dependence.

Topological and Conformational Effects on Electron Transfer Dynamics in Porphyrin-[60]Fullerene Interlocked Systems

The effect of molecular topology, and conformation on the dynamics of photoinduced electron transfer (ET) processes has been studied in interlocked electron donor-acceptor systems, specifically rotaxanes with zinc(II)-tetraphenylporphyrin (ZnP) electron donor and [60]fullerene (C(60)) as the electron acceptor. Formation or cleavage of coordinative bonds was used to induce major topological and conformational changes in the interlocked architecture. In the first approach, the tweezers-like structure created by the two ZnP stopper groups on the thread was used as a recognition site for complexation of 1,4-diazabicyclo[2.2.2]octane (DABCO), which creates a bridge between the two ZnP moieties on the rotaxane, generating a catenane structure. The photoinduced processes in the DABCO-complexed (ZnP)(2)-[2]catenate-C(60) system were compared with those of the (ZnP)(2)-rotaxane-C(60) precursor and the previously reported ZnP-[2]catenate-C(60). Steady-state emission and transient absorption studies showed that a similar multistep ET pathway emerged for rotaxanes and catenanes upon photoexcitation at various wavelengths, ultimately resulting in a long-lived ZnP(•+)/C(60) (•-) charge separated radical pair state. However, the decay kinetics of the latter states clearly reflect the topological differences between the rotaxane, the catenate, and DABCO-complexed-catenate architectures. The lifetime of the long-distance ZnP(•+)-[Cu(I)phen(2)](+)-C(60) (•-) charge separated state is more than four times longer in 3 (1.03 µs) than in 1 (0.24 µs) and approaches that in catenate 2 (1.1 µs). The results clearly showed that adoption of a catenane from a rotaxane topology inhibits the charge recombination process. In a second approach, the Cu(I) ion used as template to assemble the (ZnP)(2)-[Cu(I)phen(2)](+)-C(60) rotaxane was removed, and structural analysis suggested a major topographical change occurred, such that charge separation between the chromophores was no longer observed upon photoexcitation in nonpolar as well as polar solvents. Only ZnP and C(60) triplet excited states were observed upon laser excitation. These results highlighted the critical importance of the central Cu(I) ion for long range ET processes in these large interlocked electron donor-acceptor systems.

Measurements of quasiparticle tunneling dynamics in a band-gap-engineered transmon qubit

We have engineered the band gap profile of transmon qubits by combining oxygen-doped Al for tunnel junction electrodes and clean Al as quasiparticle traps to investigate energy relaxation due to quasiparticle tunneling. The relaxation time T1 of the qubits is shown to be insensitive to this band gap engineering. Operating at relatively low-E(J)/E(C) makes the transmon transition frequency distinctly dependent on the charge parity, allowing us to detect the quasiparticles tunneling across the qubit junction. Quasiparticle kinetics have been studied by monitoring the frequency switching due to even-odd parity change in real time. It shows the switching time is faster than 10  μs, indicating quasiparticle-induced relaxation has to be reduced to achieve T1 much longer than 100  μs.

Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture

Superconducting quantum circuits based on Josephson junctions have made rapid progress in demonstrating quantum behavior and scalability. However, the future prospects ultimately depend upon the intrinsic coherence of Josephson junctions, and whether superconducting qubits can be adequately isolated from their environment. We introduce a new architecture for superconducting quantum circuits employing a three-dimensional resonator that suppresses qubit decoherence while maintaining sufficient coupling to the control signal. With the new architecture, we demonstrate that Josephson junction qubits are highly coherent, with T2 ∼ 10 to 20  μs without the use of spin echo, and highly stable, showing no evidence for 1/f critical current noise. These results suggest that the overall quality of Josephson junctions in these qubits will allow error rates of a few 10(-4), approaching the error correction threshold.

Triazole bridges as versatile linkers in electron donor-acceptor conjugates

Aromatic triazoles have been frequently used as π-conjugated linkers in intramolecular electron transfer processes. To gain a deeper understanding of the electron-mediating function of triazoles, we have synthesized a family of new triazole-based electron donor-acceptor conjugates. We have connected zinc(II)porphyrins and fullerenes through a central triazole moiety--(ZnP-Tri-C(60))--each with a single change in their connection through the linker. An extensive photophysical and computational investigation reveals that the electron transfer dynamics--charge separation and charge recombination--in the different ZnP-Tri-C(60) conjugates reflect a significant influence of the connectivity at the triazole linker. Except for the m4m-ZnP-Tri-C(60)17, the conjugates exhibit through-bond photoinduced electron transfer with varying rate constants. Since the through-bond distance is nearly the same for all the synthesized ZnP-Tri-C(60) conjugates, the variation in charge separation and charge recombination dynamics is mainly associated with the electronic properties of the conjugates, including orbital energies, electron affinity, and the energies of the excited states. The changes of the electronic couplings are, in turn, a consequence of the different connectivity patterns at the triazole moieties.

Photoexcited state properties of H2-porphyrin/C60-based rotaxanes as studied by time-resolved electron paramagnetic resonance spectroscopy

Light-driven intramolecular electron transfer (ET) and energy transfer (EnT) processes in two rotaxanes, the first containing two free base porphyrins and C(60) fullerene moieties incorporated around a Cu(I)bisphenanthroline core ((H(2)P)(2)-Cu(I)(phen)(2)-C(60)) and a second lacking the fullerene moiety ((H(2)P)(2)-Cu(I)(phen)(2)), were studied by X-band (9.5 GHz) time-resolved electron paramagnetic resonance (TREPR) spectroscopy. The experiments were performed in frozen toluene and ethanol and different phases of the nematic liquid crystal (E-7). It is demonstrated that the ET and EnT processes in the (H(2)P)(2)-Cu(I)(phen)(2)-C(60) rotaxane in different media result in the formation of the same charge-separated state, namely (H(2)P)(2)(•+)-Cu(I)(phen)(2)(•-)-C(60), while photoexcitation of the (H(2)P)(2)-Cu(I)(phen)(2) rotaxane does not induce noticeable transfer processes in these matrices. The results are discussed in terms of the high conformational mobility of the rotaxanes, which enables changes in the molecular topography and resultant modification of the rates and routes of photoinduced processes occurring in these systems. The parameters of the transfer processes are compared with those obtained in our previous study of (ZnP)(2)-Cu(I)(phen)(2)-C(60) and (ZnP)(2)-Cu(I)(phen)(2) rotaxanes under the same experimental conditions.

Alternative demetalation method for Cu(I)-phenanthroline-based catenanes and rotaxanes

A new and less hazardous procedure for demetalation of Cu(I)-phenanthroline-based interlocked molecules, using aqueous NH(4)OH rather than toxic KCN, has been developed. The conditions are compatible with materials containing nucleophile-sensitive appended groups such as C(60), and coordinating moieties such as zinc(II)-porphyrins.

Convergent synthesis and photoinduced processes in multi-chromophoric rotaxanes

A series of [2]rotaxane materials, in which [60]fullerene is linked to a macrocycle and ferrocene (Fc) moieties are placed at the termini of a thread, both of which possess a central Cu(I)-1,10-phenanthroline [Cu(phen)(2)](+) complex, were synthesized by self-assembly using Sauvage metal template methodology. Two types of threads were constructed, one with terminal ester linkages, and a second with terminal 1,2,3-triazole linkages derived from Cu(I)-catalyzed "click" 1,3-cycloaddition reactions. Model compounds lacking the fullerene moiety were prepared in an analogous manner. The ability of the interlocked Fc-[Cu(phen)(2)](+)-C(60) hybrids to undergo electron transfer upon photoexcitation in benzonitrile, dichloromethane, and ortho-dichlorobenzene was investigated by means of time-resolved fluorescence and transient absorption spectroscopy, using excitation wavelengths directed at the fullerene and [Cu(phen)(2)](+) subunits. The energies of the electronic excited states and charge separated (CS) states that might be formed upon photoexcitation were determined from spectroscopic and electrochemical data. These studies showed that MLCT excited states of the copper complex in the fullerenerotaxanes were quenched by electron transfer to the fullerene in benzonitrile, resulting in charge separated states with oxidized copper and reduced fullerene moieties, (Fc)(2)-[Cu(phen)(2)](2+)-C(60)(•-). Even though electron transfer from Fc to the oxidized copper complex is predicted to be exergonic by 0.16 to 0.20 eV, no unequivocal evidence in support of such a process was obtained. The conclusion that Fc plays no role in the photoinduced processes in our systems rests on the lack of enhancement of the lifetime of the charge separated state, as measured by decay of C(60)(•-) at ∼1000 nm, since one-electron oxidized Fc is very difficult to detect spectroscopically in the 500-800 nm spectral region.

High-fidelity readout in circuit quantum electrodynamics using the Jaynes-Cummings nonlinearity

We demonstrate a qubit readout scheme that exploits the Jaynes-Cummings nonlinearity of a superconducting cavity coupled to transmon qubits. We find that, in the strongly driven dispersive regime of this system, there is the unexpected onset of a high-transmission "bright" state at a critical power which depends sensitively on the initial qubit state. A simple and robust measurement protocol exploiting this effect achieves a single-shot fidelity of 87% using a conventional sample design and experimental setup, and at least 61% fidelity to joint correlations of three qubits.

High-cooperativity coupling of electron-spin ensembles to superconducting cavities

Electron spins in solids are promising candidates for quantum memories for superconducting qubits because they can have long coherence times, large collective couplings, and many qubits could be encoded into spin waves of a single ensemble. We demonstrate the coupling of electron-spin ensembles to a superconducting transmission-line cavity at strengths greatly exceeding the cavity decay rates and comparable to the spin linewidths. We also perform broadband spectroscopy of ruby (Al₂O₃:Cr(3+)) at millikelvin temperatures and low powers, using an on-chip feedline. In addition, we observe hyperfine structure in diamond P1 centers.

Storage of multiple coherent microwave excitations in an electron spin ensemble

Strong coupling between a microwave photon and electron spins, which could enable a long-lived quantum memory element for superconducting qubits, is possible using a large ensemble of spins. This represents an inefficient use of resources unless multiple photons, or qubits, can be orthogonally stored and retrieved. Here we employ holographic techniques to realize 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 in excess of seconds.

Proposal for manipulating and detecting spin and orbital States of trapped electrons on helium using cavity quantum electrodynamics

We propose a hybrid architecture in which an on-chip high finesse superconducting cavity is coupled to the lateral motion and spin state of a single electron trapped on the surface of superfluid helium. We estimate the motional coherence times to exceed 15  μs, while energy will be coherently exchanged with the cavity photons in less than 10 ns for charge states and faster than 1  μs for spin states, making the system attractive for quantum information processing and strong coupling cavity quantum electrodynamics experiments. The cavity is used for nondestructive readout and as a quantum bus mediating interactions between distant electrons or an electron and a superconducting qubit.

[2]Catenanes decorated with porphyrin and [60]fullerene groups: design, convergent synthesis, and photoinduced processes

A new class of [2]catenanes containing zinc(II)-porphyrin (ZnP) and/or [60]fullerene (C(60)) as appended groups has been prepared. A complete description of the convergent synthetic approach based on Cu(I) template methodology and "click" 1,3-dipolar cycloaddition chemistry is described. This new electron donor-acceptor catenane family has been subjected to extensive spectroscopic, computational, electrochemical and photophysical studies. (1)H NMR spectroscopy and computational analysis have revealed that the ZnP-C(60)-[2]catenane adopts an extended conformation with the chromophores as far as possible from each other. A detailed photophysical investigation has revealed that upon irradiation the ZnP singlet excited state initially transfers energy to the (phenanthroline)(2)-Cu(I) complex core, producing a metal-to-ligand charge transfer (MLCT) excited state, which in turn transfers an electron to the C(60) group, generating the ZnP-[Cu(phen)(2)](2+)-C(60)(*-) charge-separated state. A further charge shift from the [Cu(phen)(2)](2+) complex to the ZnP subunit, competitive with decay to the ground state, leads to the isoenergetic long distance ZnP(*+)-[Cu(phen)(2)](+)-C(60)(*-) charge-separated radical pair state, which slowly decays back to the ground state on the microsecond time scale. The slow rate of back-electron transfer indicates that in this interlocked system, as in previously studied covalently linked ZnP-C(60) hybrid materials, this process occurs in the Marcus-inverted region.

Quantum computing with an electron spin ensemble

We propose to encode a register of quantum bits in different collective electron spin wave excitations in a solid medium. Coupling to spins is enabled by locating them in the vicinity of a superconducting transmission line cavity, and making use of their strong collective coupling to the quantized radiation field. The transformation between different spin waves is achieved by applying gradient magnetic fields across the sample, while a Cooper pair box, resonant with the cavity field, may be used to carry out one- and two-qubit gate operations.

Controlling the spontaneous emission of a superconducting transmon qubit

We present a detailed characterization of coherence in seven transmon qubits in a circuit QED architecture. We find that spontaneous emission rates are strongly influenced by far off-resonant modes of the cavity and can be understood within a semiclassical circuit model. A careful analysis of the spontaneous qubit decay into a microwave transmission-line cavity can accurately predict the qubit lifetimes over 2 orders of magnitude in time and more than an octave in frequency. Coherence times T1 and T_{2};{*} of more than a microsecond are reproducibly demonstrated.