Research Highlights 2017-01-13T16:55:17+00:00

Research Highlights and Key Outcomes

The IQIM encompasses four Major Activities (MAs) enumerated below, but the boundaries between these activities are porous and loosely defined. The MAs reinforce one another, and much of our scientific success has been derived from the interactions among the groups. Here we report on some of our significant research accomplishments for the past year.

MA-1: Quantum Information

MA-1

Figure 1. Output single-qubit probability distributions obtained by a classical simulation of the hidden shift quantum algorithm on n=40 qubits. Only one half of all qubits are shown (qubits 21,22,…,40). The final state of the algorithm is |s⟩=U|0⊗n⟩, where s is the hidden shift string to be found and U is a Clifford+T circuit with the T count t=40 (left) and t=48 (right). In both cases the circuit U contains a few hundred Clifford gates. For each qubit the probability of measuring “1” in the final state is indicated in blue. The x-axis labels indicate the correct hidden shift bits. The entire simulation took several hours on a laptop computer.

Postdoc David Gosset, with Sergey Bravyi, considered how the resources needed for classical simulation of a quantum circuit scale with the number t of T gates (rotations by angle p/4), when all the other gates are Clifford gates [1]. Their classical simulation scheme is surprisingly efficient, and may serve as a verification tool for medium-size quantum computations that are dominated by Clifford gates. Demonstrating the power of their new method, they performed a classical simulation of a hidden shift quantum algorithm with 40 qubits, a few hundred Clifford gates, and nearly 50 T-gates. See Figure 1.

1. Sergey Bravyi and David Gosset (2016) Improved Classical Simulation of Quantum Circuits Dominated by Clifford Gates. Physical Review Letters, 116 (25). Art. No. 250501. ISSN 0031-9007. http://resolver.caltech.edu/CaltechAUTHORS:20160620-110726584
Simulated quantum annealing is a Monte-Carlo algorithm, running on a classical computer, which samples the equilibrium thermal state of a quantum annealing Hamiltonian.  Elizabeth Crosson, with Aram Harrow, showed that simulated quantum annealing sometimes successfully accounts for the effects of quantum tunneling in a quantum annealer, exhibiting an exponential advantage over classical simulated annealing in which quantum tunneling is not faithfully described [2]. This work supports the growing consensus that quantum annealers are unlikely to achieve exponential speedups over classical computing solely by the use of quantum tunneling.

2. E. Crosson and A. W. Harrow, Simulated quantum annealing can be exponentially faster than classical simulated annealing, http://arxiv.org/abs/1601.03030

For any decision problem, there exists a span program leading to an algorithm with optimal quantum query complexity, but finding such an algorithm is generally challenging. Stacey Jeffery, with Tsuyoshi Ito, formulated new ways to design quantum algorithms using span programs [3]. For example, using their techniques, the span program for OR, which can be used to design an optimal algorithm for the OR function, can also be used to design optimal algorithms for threshold functions (in which we want to decide if the Hamming weight of a string is above a threshold or far below, given the promise that one of these is true), and approximate counting (in which we want to estimate the Hamming weight of the input).

3. T. Ito and Stacey Jeffery (2015) Approximate span programs, https://arxiv.org/abs/1507.00432  (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20151027-093446138

Extending their previous results, Thomas Vidick and collaborators showed that for a broad class of models (including gapped Hamiltonians with polynomial ground state degeneracy and even some classes of critical systems) ground states of one-dimensional local Hamiltonians can be found efficiently [4]. Their new algorithms bear a close resemblance to renormalization procedures, but in contrast to all previously proposed algorithms the convergence rate can be rigorously bounded. In [5] they improved and simplified one of the main tools used in [4], the so-called detectability lemma. Using the improved lemma they showed that any frustration-free gapped Hamiltonian with spectral gap ϒ can be coarse-grained, to within a length scale of order the inverse square root of ϒ, to yield a local Hamiltonian with constant spectral gap.

4. Itai Arad, Zeph Landau, Umesh Vazirani, and Thomas Vidick (2016), Rigorous RG algorithms and area laws for low energy eigenstates in 1D, http://arxiv.org/abs/1602.08828  (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20160321-072746620
5. Anurag Anshu, Itai Arad., and Thomas Vidick, (2016) A simple proof of the detectability lemma and spectral gap amplification. Physical Review B, 93 (20). Art. No. 205142. ISSN 1098-0121. http://resolver.caltech.edu/CaltechAUTHORS:20160318-153303794

MA-2: Quantum Matter Theory

MA-2 Quantum Matter Theory Research Highlight

Figure 2. Geometries utilized for the proposed milestone experiments. (a)-(d) Two-island setup with gate-tunable valves that electrically tune the Josephson-to-charging energy ratios for each pair of adjacent superconducting regions. Various interesting regimes are possible depending on the valve configurations: When cut off from the outer bulk superconductors the islands can (a) form independent double quantum dots or (b) effectively combine into a single dot. Restoring the connection to the outer superconductors quenches charging energy and generates topological superconductivity on the islands. Either two or four Majorana zero modes (denoted by x’s) appear depending on the middle-valve configuration as shown in (c) and (d). (e) Trijunction geometry that enables braiding through similar valve manipulations.

Experiments have evolved to the point where we may soon be passing from the `Majorana detection era’ to the `Majorana control era’. Graduate student Dave Aasen, working with postdoc Ryan Mishmash, Jason Alicea and collaborators in Copenhagen, introduced a new all-electrical initialization, manipulation, and readout scheme for Majorana modes in semiconducting-wire devices that leverages tools commonly used in quantum dot and spin qubit studies. They also introduced a series of milestone experiments that reveal foundational properties of Majorana modes directly relevant for quantum computing in the near future, see Figure 2. This work combined the expertise of several members of the IQIM and wouldn’t have been possible without it.

1. Aasen, David and Hell, Michael and Mishmash, Ryan V. and Higginbotham, Andrew and Danon, Jeroen and Leijnse, Martin and Jespersen, Thomas S. and Folk, Joshua A. and Marcus, Charles M. and Flensberg, Karsten and Alicea, Jason (2015) Milestones toward Majorana-based quantum computing.(Submitted) http://arxiv.org/abs/1511.05153, http://resolver.caltech.edu/CaltechAUTHORS:20160329-103533737
So far it was believed that Majorana states cannot realize a crucial gate – the pi/8 phase gate. Without this gate, a Majorana platform will have to be augmented with additional non-protected quantum circuits to form a quantum computer capable of any computation. Gil Refael, working with IQIM postdoc Torsten Karzig and collaborators Yuval Oreg and Michael Freedman, showed that a robust ‘magic’ phase gate can be achieved using NMR-like techniques. The protocol can be applied to any hardware realizing Majoranas.

2. Karzig, Torsten and Oreg, Yuval and Refael, Gil and Freedman, Michael H. (2015) A geometric protocol for a robust Majorana magic gate. (Submitted) https://arxiv.org/abs/1511.05161 http://resolver.caltech.edu/CaltechAUTHORS:20160602-064512689
Figure 1: Dirac electrons/holes bound to two vortices form dual Dirac fermions. Weakly interacting electrons correspond to strongly interacting dual fermions, i.e., QED3. A physical magnetic field is experienced by dual fermions as a chemical potential.

Figure 1: Dirac electrons/holes bound to two vortices form dual Dirac fermions. Weakly interacting electrons correspond to strongly interacting dual fermions, i.e., QED3. A physical magnetic field is experienced by dual fermions as a chemical potential.

IQIM postdoc David Mross working with Lesik Motrunich and Jason Alicea provided an explicit derivation of duality between one free Dirac cone and Quantum Electrodynamics in (2+1) dimensions (QED3), see Figure 1. This duality underlies a recent exciting conjecture by Son that composite fermions in the half-filled Landau level have Dirac character [4]. This derivation is essentially constructive and proceeds by coupling (1+1)D wires utilizing bosonization techniques and is well-controlled. In particular, they were able to make novel non-perturbative predictions for the presence and properties of a critical phase in the QED3 field theory. The same constructive approach has already yielded other interesting results – in a very recent paper Mross, Alicea and Motrunich [5] (submitted to PRL), propose an interesting bosonic analog of the Dirac composite fermi liquid.

3. Mross, David F. and Alicea, Jason and Motrunich, Olexei I. (2016) Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions. Physical Review Letters, 117 (1). Art. No. 016802. ISSN 0031-9007. http://resolver.caltech.edu/CaltechAUTHORS:20160404-083319765
4. Son, Dam Thanh (2015) Is the Composite Fermion a Dirac Particle? Phys. Rev. X 5, 031027
5. Mross, David F. and Alicea, Jason and Motrunich, Olexei I. (2016) Bosonic Analogue of Dirac Composite Fermi Liquid. Physical Review Letters, 117 (13). Art. No. 136802. ISSN 0031-9007. http://resolver.caltech.edu/CaltechAUTHORS:20160518-123950203

Symmetry fractionalization (SF) describes the fascinating phenomena that excitations in a topological system can transform under symmetry in a fractional way. For example, it is well known that in fractional quantum Hall systems, excitations can carry fractional charges while the electrons making up the system have charge one. An important realization in the study of SF is that some seemingly consistent SF patterns are actually anomalous and cannot be realized on their own. Xie Chen, with collaborator Michael Hermele, proposed a flux fusion method to detect the subtle difference between anomalous and non-anomalous SF patterns. This analysis provides deeper insight into the physics of 2D spin liquids and 3D symmetry enriched topological phases.

6.  Hermele, Michael and Chen, Xie (2015) Bosonic topological crystalline insulators and anomalous symmetry fractionalization via the flux-fusion anomaly test. http://arxiv.org/abs/1508.00573 , submitted to Phys. Rev. X http://resolver.caltech.edu/CaltechAUTHORS:20160623-123437341
7.  Chen, Xie and Hermele, Michael (2016) Symmetry fractionalization and anomaly detection in three-dimensional topological phases. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20160510-094301838

MA-2: Quantum Matter Experiment

figure from Hsieh paper broken symmetries

Fig. 3 a, The intensity of light reflected at the fundamental (I^ω) and second harmonic (I^2ω) frequencies of an obliquely incident beam is measured as a function of the angle () between the scattering plane and the a-c plane of YBa2Cu3Oy. The incident photon energy (1.5 eV) is resonant with the O 2p to Cu 3d charge transfer transition (inset). b, Polar plot of I^2ω (φ) measured below (squares; blue area) and above (red area; consistent with 2/m symmetry) the pseudogap temperature (T* ~ 110 K) of YBa2Cu3O6.92 with both the incident and reflected beams polarized perpendicular to the scattering plane (Sin–Sout geometry).

David Hsieh’s group uncovered the broken symmetries inside the pseudogap region of the high critical temperature (Tc) superconducting material YBa2Cu3Oy. Understanding the nature of the pseudogap region is widely considered to be essential for revealing the mechanism of high-Tc superconductivity in the copper oxides. Within the last few years, experiments have suggested that the pseudogap is a bona fide thermodynamic phase of matter with distinct broken symmetries. However, exactly what set of symmetries are broken, and in turn what microscopic ordering phenomenon is occurring, remain unsettled questions. Moreover, the fate of this underlying order upon transitioning from the pseudogap region into the superconducting dome is unknown. Using a second harmonic optical rotational anisotropy technique developed in Hsieh’s lab (see Fig. 3), they discovered that global inversion symmetry and all rotational symmetries of the crystal are broken across the pseudogap phase boundary. Moreover, they found that the order parameter of this pseudogap phase persists inside the superconducting dome and does not compete with either the superconducting or charge density wave order parameters. Taken together, their results drastically narrow down the list of possible candidates for the microscopic phase underlying the pseudogap region, favoring those with an odd-parity magnetic order parameter that do not arise from a competing Fermi surface instability.

Zhao, L. and Belvin, C. A. and Liang, R. A. Bonn, W. N. Hardy, N. P. Armitage and D. Hsieh (2016) A global inversion-symmetry-broken phase inside the pseudogap region of YBa_2Cu_3O_y. Nature Physics . ISSN 1745-2473. (In Press)  http://resolver.caltech.edu/CaltechAUTHORS:20161014-080142438
Nai-Chang Yeh’s group developed single-step process for room-temperature PECVD growth of large-area, high-mobility and nearly strain-free graphene, which would allow realizing graphene-based valleytronics when combined with modern nanoscale fabrication technology, to produce strained graphene. The strain can induce giant pseudo-magnetic fields (or equivalently, giant Berry connections) that couple to the two inequivalent valleys with opposite signs, which leads to valley polarization under an applied electric field. Thus, controlled strain on perfect graphene can be tailored to yielding the desirable electronic properties for valleytronic applications.

2. Yeh, N.-C. and Hsu, C.-C. and Teague, M. L. et al. (2016) Nanoscale strain engineering of graphene and graphene-based devices. Acta Mechanica Sinica . pp. 1-13. ISSN 0567-7718. (In Press) http://resolver.caltech.edu/CaltechAUTHORS:20160217-102636750
Figure 2: (a) Device structure for hexagonal boron nitride (h-BN) tunnel devices with Cr/Au electrodes. (b) An optical micrograph of a thin hBN flake. Dotted line shows the thin region of interest. (c) hBN flake transferred on to a set of bottom electrodes. (d) Tunnel device with the horizontal top electrode forming multiple tunnel junctions, one of which is marked as a box. Scale bar is 10 μm.

Figure 2: (a) Device structure for hexagonal boron nitride (h-BN) tunnel devices with Cr/Au electrodes. (b) An optical micrograph of a thin hBN flake. Dotted line shows the thin region of interest. (c) hBN flake transferred on to a set of bottom electrodes. (d) Tunnel device with the horizontal top electrode forming multiple tunnel junctions, one of which is marked as a box. Scale bar is 10 μm.

Tunneling spectroscopy provides a tool to probe the density of states of various electronic materials. IQIM postdoctoral scholar Chandni U working with Jim Eisenstein and collaborators, explored vertical tunneling transport in van der Waals heterostructures with hexagonal boron nitride (hBN) as a tunnel barrier between graphene (or graphite) and a metal (Cr/Au) electrode. They observed a strong suppression of tunneling at low biases, with a gap of about 130 meV in the dI/dV spectrum for metal-hBN-graphene (or graphite) structures. In the graphene devices, the finite zero-bias tunnel resistance was found to depend on the electron density of the graphene layer, while the gap remained unaffected. They also tested graphite-hBN-graphite junctions, in which the strong suppression of tunneling at low energies was found to be absent. See Figure 2.

3. Chandni, U. and Watanabe, K. and Taniguchi, T. et al. (2015) Evidence for defect-mediated tunneling in hexagonal boron nitride-based junctions. Nano Letters, 15 (11). pp. 7329-7333. ISSN 1530-6984. http://resolver.caltech.edu/CaltechAUTHORS:20151015-094529168

MA-3: Quantum Optics

The Kimble group has made important advances at the interface of nano-photonics, atomic physics, and quantum optics. They have demonstrated a new avenue for tailoring the interactions between quantum emitters and single photons [1], which constitutes a cornerstone of quantum optics. Coupling a quantum emitter to the band edge of a photonic crystal waveguide (PCW) provides a unique platform for tuning these interactions. In particular, the crossover from propagating fields outside the bandgap to exponentially localized fields within the bandgap should be accompanied by a transition from largely dissipative atom-atom interactions to a regime where dispersive atom-atom interactions are dominant. They observed this transition for the first time by shifting the band edge frequency of a PCW relative to the D1 line of atomic Cesium for an average number ~ 3 atoms trapped along a PCW [2]. The foundation for the analysis of these experiments is a new formalism for atom-photon physics in nano-photonic lattices developed with colleagues at the Institute for Photonic Sciences (ICFO) [2].

1. J. D. Hood, A. Goban, A. Asenjo-Garcia, M. Lu, S.-P. Yu, D. E. Chang, and H. J. Kimble, Atom-atom interactions around the band edge of a photonic crystal waveguide, Proceedings of the US National Academy of Sciences (PNAS) (2016); available as arXiv:1603.02771v1.
2. A. Asenjo-Garcia, J. D. Hood, D. E. Chang, and H. J. Kimble, Atom-light interactions in quasi-1D nanostructures: a Green’s function perspective, New Journal of Physics (in review, 2016); available at http://arxiv.org/abs/1606.04977.
Figure 3: SEM images of the fabricated nanobeam resonators. (a) Devices for different spectrum range with identical structure features but different global scaling factors. (b) The fabricated device in YVO crystal, which has the same geometric structures as devices in YSO. The side-view in (c) shows the non-vertical sidewalls due to FIB beam divergence, which can be improved by varying the ion beam voltage and current. The top-view in (d) reveals the grooves on a thin support beam. The triangular cross-section of the beam is seen in (e).

Figure 3: SEM images of the fabricated nanobeam resonators. (a) Devices for different spectrum range with identical structure features but different global scaling factors. (b) The fabricated device in YVO crystal, which has the same geometric structures as devices in YSO. The side-view in (c) shows the non-vertical sidewalls due to FIB beam divergence, which can be improved by varying the ion beam voltage and current. The top-view in (d) reveals the grooves on a thin support beam. The triangular cross-section of the beam is seen in (e).

Numerous bulk crystalline materials exhibit attractive nonlinear and luminescent properties for classical and quantum optical applications. For instance, erbium dopants in crystals exhibit highly coherent optical transitions well suited for solid-state optical quantum memories operating in the telecom band. A chip-scale platform for high quality factor optical nanocavities in these materials will enable new optoelectronic devices and quantum light-matter interfaces. The Faraon group has recently [3, 4] been able to create photonic crystal nanobeam resonators fabricated using focused ion beam milling in bulk insulators, such as rare-earth doped yttrium orthosilicate and yttrium vanadate (see Figure 3). Operation in the visible, near infrared, and telecom wavelengths with quality factors up to 27,000 and optical mode volumes close to one cubic wavelength were demonstrated. Critically, the Faraon group showed coupling of erbium ions to the modes of a photonic crystal cavity, which led to a measured reduction of the photoluminescence lifetime and enhancement of the optical depth in microns-long devices. Such advancements will enable on-chip quantum memories utilizing these erbium doped cavities.

3. Zhong, Tian and Rochman, Jake and Kindem, Jonathan M. and Miyazono, Evan and Faraon, Andrei (2016) High quality factor nanophotonic resonators in bulk rare-earth doped crystals. Optics Express, 24 (1). pp. 536-544. ISSN 1094-4087. http://resolver.caltech.edu/CaltechAUTHORS:20160204-130436067
4. Miyazono, Evan and Zhong, Tian and Craiciu, Ioana et al. (2016) Coupling of erbium dopants to yttrium orthosilicate photonic crystal cavities for on-chip optical quantum memories. Applied Physics Letters, 108 (1). Art. No. 011111. ISSN 0003-6951. http://resolver.caltech.edu/CaltechAUTHORS:20160119-093504030

MA-4: Mechanical Quantum Systems

Figure 4: (A) Schematic showing frequencies of squeezing drive tones relative to the cavity frequency. (B) Optical micrograph of a typical device. Grey regions are aluminum, and blue regions are the exposed silicon substrate. The center square is a parallel-plate capacitor with a top plate that has a mechanical degree of freedom. (C) Microwave circuit diagram for squeezing measurements. The red- and blue-detuned tones are filtered at room temperature and attenuated at low temperatures so that they are shot-noise limited at the device. The device is thermally connected to the mixing plate of a dilution refrigerator.

Figure 4: (A) Schematic showing frequencies of squeezing drive tones relative to the cavity frequency. (B) Optical micrograph of a typical device. Grey regions are aluminum, and blue regions are the exposed silicon substrate. The center square is a parallel-plate capacitor with a top plate that has a mechanical degree of freedom. (C) Microwave circuit diagram for squeezing measurements. The red- and blue-detuned tones are filtered at room temperature and attenuated at low temperatures so that they are shot-noise limited at the device. The device is thermally connected to the mixing plate of a dilution refrigerator.

The Schwab group has demonstrated “squeezing” of the motion of a micrometer-sized mechanical system (see Figure 4). By driving up the fluctuations in one of the quadratures of the system, they were able to squeeze the fluctuations in the other quadrature. Using the usually feeble force associated with radiation pressure from a microwave source connected to a capacitor on the mechanical system, Schwab and his team manipulated the thermal fluctuations of a micrometer-scale mechanical resonator to produce a stationary quadrature-squeezed state with a minimum variance of 0.80 times that of the ground state uncertainty given by the quantum zero-point motion amplitude. They also performed phase-sensitive, back-action evading measurements of a thermal state squeezed to 1.09 times the zero-point level. These results are relevant to the quantum engineering of states of matter at large length scales, the study of decoherence of large quantum systems, and for the realization of ultrasensitive sensing of force and motion.

1. Wollman, E. E. and Lei, C. U. and Weinstein, A. J. and Suh, J. and Kronwald, A. and Marquardt, F. and Clerk, A. A. and Schwab, K. C. (2015) Quantum squeezing of motion in a mechanical resonator. Science, 349 (6251). pp. 952-955. ISSN 0036-8075. http://resolver.caltech.edu/CaltechAUTHORS:20150728-095253969
Figure 4: SEM image of an optomechanical crystal circuit on a SOI microchip. The circuit consists of optical input/output (I/O) ports for driving the circuit optically, a left and right optomechanical cavity where radiation pressure couples the light field to internal vibrational (phonon) modes in the microwave X-band, and an intermediate phononic crystal waveguide which couples phonons from one cavity to the other.

Figure 4: SEM image of an optomechanical crystal circuit on a SOI microchip. The circuit consists of optical input/output (I/O) ports for driving the circuit optically, a left and right optomechanical cavity where radiation pressure couples the light field to internal vibrational (phonon) modes in the microwave X-band, and an intermediate phononic crystal waveguide which couples phonons from one cavity to the other.

So far most experimental achievements in the field of cavity-optomechanics have been realized in setups comprising one optical mode coupled to one vibrational mode. One of the next frontiers is the combination of many such optomechanical cells into an optomechanical array, enabling the optical in situ investigation of (quantum) many-body dynamics of interacting photons and phonons. In collaboration with theorists at the University of Erlangen, the Painter group has analyzed in a new paper [2] how the optomechanical interaction between photons and mechanical vibrations can be used to create artificial magnetic fields for photons on a lattice. In two related experimental efforts [3, 4] the Painter group has also shown just how feasible such experiments may be in the near future. In the first experiment [3], Painter and his team created for the first time a cavity-optomechanical circuit consisting of multiply connected cavity elements via photon and phonon waveguides on a silicon microchip (see Figure 4). In the second experiment, individual optomechanical crystal cavities were measured at milliKelvin temperatures using optical probing techniques and single photon counting. These measurements showed that such optomechanical devices could be cooled deep in the quantum regime (thermal occupany) with extremely long thermal decoherence times approaching a millisecond.

2. M. Schmidt, S. Keßler, V. Peano, O. Painter, and F. Marquardt (2015) Optomechanical creation of magnetic fields for photons on a lattice, Optica, DOI: 10.1364/OPTICA.2.000635, July 10, 2015. http://resolver.caltech.edu/CaltechAUTHORS:20150317-084906162
3. Kejie Fang, Matthew M. Matheny, Xingsheng Luan, and Oskar Painter (2016) Optical transduction and routing of microwave phonons in cavity-optomechanical circuits, Nature Photonics, DOI:10.1038/NPHOTON.2016.107,June 13, 2016. http://resolver.caltech.edu/CaltechAUTHORS:20160422-124451220
4. Sean M. Meenehan, Justin D. Cohen, Gregory S. MacCabe, Francesco Marsili, Matthew D. Shaw, and Oskar Painter (2015) Pulsed excitation dynamics of an optomechanical crystal resonator near its quantum ground-state of motion, Phys. Rev. X, DOI: 10.1103/PhysRevX.5.041002, October 6, 2015. http://resolver.caltech.edu/CaltechAUTHORS:20150317-184439024