Mohammad Hafezi

Joint Quantum Institue, UMD/NIST, IREAP · PHYS/ECE

We present a reconfigurable topological photonic system consisting of a 2D lattice of coupled ring resonators, with two sublattices of site rings coupled by link rings, which can be accurately described by a tight-binding model. Unlike previous coupled-ring topological models, the design is translationally invariant, similar to the Haldane model, a...

We find that next-nearest-neighbour coupling in ring resonator lattices induces topological transitions and one-way edge modes. We design topological waveguides that are easily switchable using thermal, electro-optic, or nonlinear effects, enabling robust on-chip photon routing.

We theoretically study the transport of time-bin entangled photon pairs in a two-dimensional topological photonic system of coupled ring resonators. This system implements the integer quantum Hall model using a synthetic gauge field and exhibits topologically robust edge states. We show that the transport through edge states preserves temporal corr...

A hallmark feature of topological physics is the presence of one-way propagating chiral modes at the system boundary. The chirality of edge modes is a consequence of the topological character of the bulk. For example, in a non-interacting quantum Hall model, edge modes manifest as mid-gap states between two topologically distinct bulk bands. The bu...

We study transport of entangled photons in a topological system of coupled-ring resonators and show that the edge states could enable robust on-chip quantum communication channels. We report on the experimental progress towards this demonstration.

Usually photons are not conserved in their interaction with matter. Consequently, for the thermodynamics of photons, while we have a concept of temperature for energy conservation, there is no equivalent chemical potential for particle number conservation. However, the notion of a chemical potential is crucial in understanding a wide variety of sin...

Simulations reveal that microwaves propagating through a waveguide can travel around sharp bends in the device without being reflected. The finding might open the way to technologies that exploit this uncommon phenomenon.

Topological Quantum Field Theories (TQFTs) are powerful tools to describe universal features of topological orders. A hallmark example of a TQFT is the 2+1 D Chern-Simons (CS) theory which describes topological properties of both integer and fractional quantum Hall effects. The gauge invariant form of the CS theory with boundaries, encompassing bot...

We propose a method of measuring topological invariants of a photonic crystal through phase spectroscopy. We show how the Chern numbers can be deduced from the winding numbers of the reflection coefficient phase. An explicit proof of existence of edge states in system with nonzero reflection phase winding number is given. The method is illustrated...

A quantum simulator of U(1) lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transition...

We suggest a scheme for the preparation of highly correlated Laughlin (LN) states in the presence of synthetic gauge fields, realizing an analogue of the fractional quantum Hall effect in photonic or atomic systems of interacting bosons. It is based on the idea of growing such states by adding weakly interacting composite fermions (CF) along with m...

Photons are not conserved in interactions with other matter. Consequently, when understanding the equation of state and thermodynamics of photons, while we have a concept of temperature for energy conservation, there is no equivalent chemical potential for particle number conservation. However, the notion of a chemical potential is crucial in under...

Electrons in a so-called topological insulator circulate around the material’s boundary without ever straying into the bulk. Uncharged photons can be induced to carry out similar behavior.

Electronic transport in low dimensions through a disordered medium leads to localization. The addition of gauge fields to disordered media leads to fundamental changes in the transport properties. For example, chiral edge states can emerge in two-dimensional systems with a perpendicular magnetic field. Here, we implement a "synthetic'' gauge field...

We show how engineered classical noise can be used to generate constrained Hamiltonian dynamics in atomic quantum simulators of many-body systems, taking advantage of the continuous Zeno effect. After discussing the general theoretical framework, we focus on applications in the context of lattice gauge theories, where imposing exotic, quasi-local c...

Recent progress in nanoscale quantum optics and superconducting qubits has made the creation of strongly correlated, and even topologically ordered, states of photons a real possibility. Many of these states are gapped and exhibit anyon excitations, which could be used for a robust form of quantum information processing. However, while numerous qub...

Resistance thermometry provides a time-tested method for taking temperature measurements. However, fundamental limits to resistance-based approaches has produced considerable interest in developing photonic temperature sensors to leverage advances in frequency metrology and to achieve greater mechanical and environmental stability. Here we show tha...

In this article, we review the recent progress in the implementation of synthetic gauge fields for photons and the investigation of new photonic phenomena, such as non-equilibrium quantum Hall physics. In the first part, we discuss the implementation of magnetic-like Hamiltonians in coupled resonator systems and provide a pedagogical connection bet...

Electronic transport is localized in low-dimensional disordered media. The addition of gauge fields to disordered media leads to fundamental changes in the transport properties. We implement a synthetic gauge field for photons using silicon-on-insulator technology. By determining the distribution of transport properties, we confirm that waves are l...

Topological features—global properties not discernible locally—emerge in systems ranging from liquid crystals to magnets to fractional quantum Hall systems. A deeper understanding of the role of topology in physics has led to a new class of matter—topologically ordered systems. The best known examples are quantum Hall effects, where insensitivity t...

We demonstrate a scheme to engineer the three-body interaction in circuit-QED systems by tuning a fluxonium qubit. Connecting such qubits in a square lattice and controlling the tunneling dynamics, in the form of a synthesized magnetic field, for the photon-like excitations of the system, allows the implementation of a parent Hamiltonian whose grou...

Temperature needs to be controlled accurately and precisely in various areas, yet it is one of the most inaccurately measured physical quantities. We consider a new measurement method for temperature using the thermal response of a microring resonator built using Silicon-on-Insulator. The temperature-dependence of the index refraction maps temperat...

To create a hybrid quantum system, we plan to trap neutral atoms in the evanescent optical field from an optical nanofiber and move them to within a few microns above a SQUID in a dilution refrigerator that operates at 10 mK. A key component in this experiment is a long section (10 cm) of optical fiber with a uniform diameter of about 500 nm, suffi...

We present progress toward a hybrid quantum system in which microwave quanta stored in a superconducting flux qubit are coupled through a magnetic dipole interaction to laser-trapped atoms. In initial experiments, our goal will be to couple a microfabricated superconducting LC resonator to the 6.835 GHz hyperfine splitting in an ensemble of ^87Rb a...

We have developed a tunable ``lumped-element" thin-film superconducting Al microwave resonator [1] and used it for measuring two level systems. The device is intended for coupling to the hyperfine splitting of trapped ^87Rb atoms at 6.83 GHz. By moving a superconducting Al pin towards the inductor of the resonator using a piezo stage, we can tune t...

We propose a solid-state architecture to quantum simulate dynamical lattice gauge-field theories [1, 2]. Specifically, we consider a superconducting-circuit implementation of U(1) quantum link models [3], where the gauge fields can be expressed in terms of spin operators. We show that a general gauge-invariant Hamiltonian [2] can be simulated using...

Systems with topological order exhibit exotic phenomena associated purely with the boundaries of the system. While most systems with topological order have been electronic, advances in our understanding of synthetic gauge fields have enabled investigation of topological order in ultracold atoms or even with photons. Here, we demonstrate the experim...

One approach to quantum information processing is to use photons as quantum bits and rely on linear optical elements for most operations. However, some optical nonlinearity is necessary to enable universal quantum computing. Here, we suggest a circuit-QED approach to nonlinear optics quantum computing in the microwave regime, including a determinis...

We investigate the quantum dynamics of systems involving small numbers of strongly interacting photons. Specifically, we develop an efficient method to investigate such systems when they are externally driven with a coherent field. Furthermore, we show how to quantify the many-body quantum state of light via correlation functions. Finally, we apply...

We review our recent experiments demonstrating a hollow-core photonic-crystal fiber loaded with laser-cooled atomic vapor as a system for all-optical switching with pulses containing few hundred photons. Additionally, we discuss the outlooks for improving the efficiency of this switching scheme and present preliminary results geared toward using th...

Nanofibers are a promising tool for hybrid systems of atomtronics and quantum information. We present the construction and characterization protocol that allows us to reliably produce nanofibers with a waist up to 10 cm in length and down to 500 nm in diameter operating around 780 nm (Rb D2 line). By controlling the angle in the tapered region at c...

We have constructed a robust system for studying atom-light interactions in atomtronics and hybrid quantum information. We require the loading of atomic dipole traps formed on tapered optical nanofibers and other photonic structures from magneto-optical traps. A commercially available UHV manipulator allows for controlled translation of the structu...

We describe a new approach for on-chip optical non-reciprocity which makes use of strong optomechanical interaction in microring resonators. By optically pumping the ring resonator in one direction, the optomechanical coupling is only enhanced in that direction, and consequently, the system exhibits a non-reciprocal response. For different configur...

We have developed a frequency tuning system for a ``lumped-element'' thin-film superconducting Al microwave resonator [1] on sapphire intended for coupling to hyperfine ground states of cold trapped ^87Rb atoms, which are separated by about fRb=6.83 GHz. At T=12 mK and on resonance at 6.81 GHz, the loaded quality factor was 120,000. By moving a car...

Phenomena associated with the topological properties of physical systems can be naturally robust against perturbations. This robustness is exemplified by quantized conductance and edge state transport in the quantum Hall and quantum spin Hall effects. Here we demonstrate how quantum spin Hall Hamiltonians can be simulated with linear optical elemen...

A complete physical approach to quantum information requires a robust interface among flying qubits, long-lifetime memory and computational qubits. Here we present a unified interface for microwave and optical photons, potentially connecting engineerable quantum devices such as superconducting qubits at long distances through optical photons. Our a...

We describe a thin-film superconducting Nb microwave resonator, tunable to within 0.3 ppm of the hyperfine splitting of $^{87}$Rb at $f_{Rb}=6.834683$ GHz. We coarsely tuned the resonator using electron-beam lithography, decreasing the resonance frequency from 6.8637 GHz to 6.8278 GHz. For \emph{in situ} fine tuning at 15 mK, the resonator inductan...

We present a scheme to couple trapped $^{87}$Rb atoms to a superconducting flux qubit through a magnetic dipole transition. We plan to trap atoms on the evanescent wave outside an ultrathin fiber to bring the atoms to less than 10 $\mu$m above the surface of the superconductor. This hybrid setup lends itself to probing sources of decoherence in sup...

Recent proposals in quantum computing center on the creation of hybrid quantum processors. Here we report progress on an experiment to couple an ensemble of ^87Rb atoms to a superconducting, thin-film LC resonator at 20 mK through a magnetic dipole transition. We have demonstrated tuning of the LC resonator to within 2 kHz of the 6.8GHz hyperfine s...

One approach to quantum information processingootnotetext``A Scheme for Efficient Quantum Computation with Linear Optics,'' E. Knill, R. Laflamme, G.J. Milburn (Nature, Vol 409, 4 January 2001) is to use photons as quantum bits and rely on the robustness of linear optical elements. However, some optical non-linearity is necessary to enable universa...

We theoretically study the transmission of few-photon quantum fields through a strongly nonlinear optical medium. We develop a general approach to investigate nonequilibrium quantum transport of bosonic fields through a finite-size nonlinear medium and apply it to a recently demonstrated experimental system where cold atoms are loaded in a hollow-c...

We present a scheme and our advances to magnetically couple 87Rb atoms to a superconducting flux qubit by trapping the atoms in the evanescent wave outside an tapered optical fiber.

Topological properties of systems lead to remarkable robustness against disorder. The hallmark of such behavior is the quantized quantum Hall effect, where the electronic transport in two-dimensional systems is protected against scattering from impurities and the quantized Hall conductance is the manifestation of a topological invariance. Here we s...

Phenomena associated with topological properties of physical systems are naturally robust against perturbations. This robustness is exemplified by quantized conductance and edge state transport in the quantum Hall and quantum spin Hall effects. Here we show how exploiting topological properties of optical systems can be used to implement robust pho...

We present a scheme and our advances to magnetically couple Rb atoms to a superconducting flux qubit by trapping the atoms in the evanescent wave outside an tapered optical fiber.

One of the major advances needed to realize all-optical information processing of light is the ability to delay or coherently store and retrieve optical information in a rapidly tunable manner. In the classical domain, this optical buffering is expected to be a key ingredient to managing the flow of information over complex optical networks. Such a...

We propose a 2D photonic system where the dynamics of photons are analogous to charged bosons in a magnetic field. We show that a magnetic field can be `simulated' for photons without using a magnetic field or any time-reversal symmetry breaking mechanism. We apply a technique to probe transport properties of such systems. In particular, the underl...

Optomechanical systems provide an intriguing test bed for examining concepts such as cooling a macroscopic quantum system to its ground state, and also for practical applications like squeezing and quantum information processing. A key difficulty at present is the weakness of the radiation pressure force in the optical domain at the single photon l...

We demonstrate a fiber-optical switch that operates with a few hundred photons per switching pulse. The light-light interaction is mediated by laser-cooled atoms. The required strong interaction between atoms and light is achieved by simultaneously confining photons and atoms inside the microscopic hollow core of a single-mode photonic-crystal fibe...

We present a theoretical technique for solving the quantum transport problem of a few photons through a one-dimensional, strongly nonlinear waveguide. We specifically consider the situation where the evolution of the optical field is governed by the quantum nonlinear Schr\"odinger equation (NLSE). Although this kind of nonlinearity is quite general...

We theoretically study the transmission of few-photon quantum fields through a strongly nonlinear optical medium. We develop a general approach to investigate non-equilibrium quantum transport of bosonic fields through a finite-size nonlinear medium and apply it to a recently demonstrated experimental system where cold atoms are loaded in a hollow-...

We demonstrate a fiber-optical switch that is activated at tiny energies corresponding to few hundred optical photons per pulse. This is achieved by simultaneously confining both photons and a small laser-cooled ensemble of atoms inside the microscopic hollow core of a single-mode photonic-crystal fiber and using quantum optical techniques for gene...

We examine the quantum transport properties of a few photons inside a one-dimensional nonlinear waveguide when the evolution is determined by the quantum nonlinear Schrodinger equation. The tight transverse confinement of the photonic modes enables a large atom-field coupling strength. Therefore, by coupling light to atoms loaded in a fiber, such a...

Cold atoms confined inside a hollow-core photonic-crystal fiber with core diameters of a few photon wavelengths are a promising medium for studying nonlinear optical interactions at extremely low light levels. The high electric field intensity per photon and interaction lengths not limited by diffraction are some of the unique features of this syst...

Cold atoms confined inside a hollow core photonic crystal fiber are a promising medium for studying nonlinear optical interactions at extremely low light levels. For instance, we demonstrated in recent experiments how such an atomic ensemble consisting of ˜10^3 laser cooled ^87Rb atoms results in an optically dense medium whose transparency can be...

We demonstrate optical nonlinearities due to the interaction of weak optical fields with the collective motion of a strongly dispersive ultracold gas. The combination of a recoil-induced resonance in the high gain regime and optical waveguiding within the dispersive medium enables us to achieve a collective atomic cooperativity of 275+/-50 even in...

We present a theoretical investigation of a photonic system obeying the quantum non-linear Schr"odinger equation in a finite size system. Such systems are now being implemented using a hollow-core fiber loaded with trapped alkali atoms. The tight transverse confinement of the photonic modes enables a large atom-field coupling strength. We investiga...

Strongly correlated quantum systems can exhibit exotic behaviour called topological order which is characterized by non-local correlations that depend on the system topology. Such systems can exhibit remarkable phenomena such as quasiparticles with anyonic statistics and have been proposed as candidates for naturally error-free quantum computation....

We study Chern numbers to characterize the ground state of strongly interacting systems on a lattice. This method allows us to perform a numerical characterization of bosonic fractional quantum Hall (FQH) states on a lattice where the conventional overlap calculation with the known continuum case such as the Laughlin state, breaks down due to the l...

We analyze a recently proposed method to create fractional quantum Hall (FQH) states of atoms confined in optical lattices [ A. Sørensen et al. Phys. Rev. Lett. 94 086803 (2005)]. Extending the previous work, we investigate conditions under which the FQH effect can be achieved for bosons on a lattice with an effective magnetic field and finite on-s...

We analyze a recently proposed method to create fractional quantum Hall (FQH) states of atoms confined in optical lattices [A. S{\o}rensen {\it et al.}, Phys. Rev. Lett. {\bf 94} 086803 (2005)]. Extending the previous work, we investigate conditions under which the FQH effect can be achieved for bosons on a lattice with an effective magnetic field...

We study Chern numbers to characterize the ground state of strongly interacting systems on a lattice. This method allows us to perform a numerical characterization of bosonic fractional quantum Hall (FQH) states on a lattice where conventional overlap calculation with known continuum case such as Laughlin state, breaks down due to the lattice struc...

We propose a whole family of physical states that yield a violation of the Bell CHSH inequality arbitrarily close to its maximum value, when using quadrature phase homodyne detection. This result is based on a new binning process called root binning, that is used to transform the continuous variables measurements into binary results needed for the...