Prof. Claudio Chamon, Boston University

Circuit complexity and functionality: a thermodynamic perspective

We explore a link between complexity and physics for circuits of given functionality. Taking advantage of the connection between circuit counting problems and the derivation of ensembles in statistical mechanics, we tie the entropy of circuits of a given functionality and fixed number of gates to circuit complexity. We use thermodynamic relations to connect the quantity analogous to the equilibrium temperature to the exponent describing the exponential growth of the number of distinct functionalities as a function of complexity. This connection is intimately related to the finite compressibility of typical circuits. Finally, we use the thermodynamic approach to formulate a framework for the obfuscation of programs of arbitrary length – an important problem in cryptography – as thermalization through recursive mixing of neighboring sections of a circuit, which can viewed as the mixing of two containers with “gases of gates”. This recursive process equilibrates the average complexity and leads to the saturation of the circuit entropy, while preserving functionality of the overall circuit. The thermodynamic arguments hinge on ergodicity in the space of circuits which we conjecture is limited to disconnected ergodic sectors due to fragmentation. The notion of fragmentation has important implications for the problem of circuit obfuscation as it implies that there are circuits with same size and functionality that cannot be connected via local moves. Furthermore, we argue that fragmentation is unavoidable unless the complexity classes NP and coNP coincide.

Dr. Paul M. Eugenio, University of Connecticut

Tunable moire sublattices in twisted square homobilayers: exploiting fundamental principles for new technologies

Stacking and twisting atomically thin bilayers at small angles produces an approximate periodic pattern, due to the overlap of the crystal layers. These devices, dubbed “moire” bilayers, exhibit a high degree of tunability and variability: through choice of twist angle, constituent layers, and gating. To date, a number of such devices have been built which have demonstrated a plethora of novel phases, including non-trivial topology and Mott physics. Despite this explosion in moire research, moire bilayers have been almost exclusively formed from layers with triangular/hexagonal crystal geometry, and where the valence bands are centered on the Gamma or K/K’ high symmetry points. Here we theoretically demonstrate that moire devices formed from square bilayers can be used to simulate the ground state of the Hubbard model, but where the ratio of the nearest-neighbor (t) and next-to-nearest neighbor (t’) tunneling can be tuned between zero and infinity, in situ via an electric field. If experimentally realized, such a device would be the first of its kind, and would open a pathway toward the testing of a number of proposed exotic phases, such as a spin-liquid and d+id superconductivity. Most importantly, the square Hubbard model is a quintessential model for high-Tc in cuprates, where numerics has demonstrated the absence of superconductivity when t’=0.

Dr. J. I. A. Li, Brown University

The Superconducting Diode Effect And Spontaneous Symmetry Breaking In Multi-Layer Graphene

The superconducting diode effect, defined as nonreciprocity in the critical supercurrent, provides a unique window into the nature of the superconducting phase. It has been argued that a zero-field diode effect in the superconducting transport requires inversion and time-reversal symmetries to be simultaneously broken. Along this vein, the zero-field superconducting diode effect in multi-layer graphene provides direct evidence of the microscopic coexistence between superconductivity and time-reversal symmetry breaking. In this talk, I will discuss our recent efforts that utilize the angle-resolved measurement of transport nonreciprocity to directly probe the nature of spontaneous symmetry breaking in the normal phase. By investigating the interplay between transport nonreciprocity, ferromagnetism, and superconductivity, our findings suggest that the exchange-driven instability in the momentum space plays a key role in the zero-field superconducting diode effect.

Prof. Jed Pixley, Rutgers University

Novel Strongly Correlated Phases in Stacked TMD Bilayers

Two-dimensional transition metal dichalcogenides (TMDs) have emerged as an exciting platform to stack and twist bilayers to engineer strongly correlated quantum phases. Here we present a theory to describe the recent realization of a heavy fermion state in stacked MoTe2/WSe2 bilayers. An extension of this theory that allows for the formation of unconventional superconductivity through repulsive nearest neighbor interactions will be used to show how to realize the p-wave BEC to BCS transition.

Dr. Jon Curtis, UCLA

Multimode cavity control of ferroelectric fluctuations

Electromagnetic cavities and metamaterials have been used to great effect in the field of AMO physics and electrical engineering. By shaping the spatial, spectral, or polarization characteristics of the electromagnetic environment, the coherent interaction between light and matter can be focused and amplified, leading to phenomena such as lasing, the Purcell effect, the Casimir effect, and superradiance. In this talk I will show how these ideas may be extended and applied to solid state quantum materials. In particular, I will consider polarization fluctuations in a quantum paraelectric insulator, and consider their coupling to a Fabry-Perot type optical cavity. By using the full multimode continuum description of the system, I will show how the ferroelectric fluctuations respond in a local, spatially resolved manner. The presence of the cavity indeed is shown to renormalize the soft-mode frequency, with effects primarily confined to the surface, and thus for thin films this effect can be pronounced. The temperature dependence shows this effect only onsets at low temperatures, indicating its origin from quantum electrodynamics effects – in close analogy with the Casimir effect.

Prof. Alicia Kollár, University of Maryland

Lattices in Circuit QED

The field of circuit QED has emerged as a rich platform for both quantum computation and quantum simulation. These systems exhibit a high degree of both spatial and temporal control which can be used to create synthetic lattice systems. Spatial lattices can be formed using periodic arrays of resonators. Combined with strong qubitphoton interactions, these systems can be used to study dynamical phase transitions, many-body phenomena, and spin models in driven-dissipative systems. I will show that lattices of coplanar waveguide (CPW) resonators permit the creation of unique devices which host photons in curved spaces, gapped flat bands, and novel forms of qubit-qubit interaction [1,2]. I will show that graph theory is the natural language for describing these microwave photonic systems and present preliminary data on the development of a new generation of CPW lattice devices with unconventional band structures. Periodic modulation in superconducting-qubit systems also provides a route to Floquet systems with topological band structures. I will present preliminary experimental steps toward the realization of a topological energy pump which can “boost” smaller non-clalssical states of light into larger ones [3].

[1] A. J. Koll´ar et al., Nature 45, 571 (2019).

[2] A. J. Koll´ar et al., Comm. Math. Phys. 376, 1909 (2020).

[3] D. Long et al., Phys. Rev. Lett. 128, 183602 (2022).

Prof. Steve Lamoreaux, Yale University

Title: TBA

Prof. Tigran Sedrakyan, University of Massachusetts Amherst

Moat-band physics and emergent excitonic topological order in correlated electron-hole bilayers”

The role of the particle-particle interaction becomes increasingly important if the spectral band structure of a free system has increasing degeneracy. Ultimately, it will be the role of interactions to choose the state of the system. Examples include the systems with the lowest band having a degenerate minimum along a closed contour in the reciprocal space – the Moat. Any weak perturbation can set a new energy scale describing the state with qualitatively different properties in such a limit of infinite degeneracy. In this talk, I will discuss the general principles behind the universal properties of correlated bosons on moat bands, which host topological order with long-range quantum entanglement. In particular, I will discuss moat-band phenomena in shallowly inverted InAs/GaSb quantum wells, where we observe an unconventional time-reversal-symmetry breaking excitonic ground state under imbalanced electron and hole densities. I will show that the strong frustration of the system leads to a moat band for excitons, resulting in a time-reversal-symmetry breaking excitonic topological order, which explains all our experimental observations.

Prof. Cyrus Dreyer, Stony Brook University and Flatiron Institute

Nonadiabatic lattice dynamics in metals and magnets

In electronic structure theory, lattice vibrations are usually treated under the Born-Oppenheimer approximation, where electronic degrees of freedom are assumed to be fast compared to nuclear dynamics. However, going beyond this adiabatic approximation is necessary in many situations for an accurate description of phonons, and their effects on materials properties. I will discuss two such cases. The first case involves Born effective charges, which are crucial to understanding, e.g., ferroelectric polarization, phonon dispersions in ionic insulators, electron-phonon scattering, dielectric screening, electromechanical coupling, and optical spectra in the IR/THz regime. Via density-functional perturbation theory (DFPT) calculations, I will show that going beyond the adiabatic approximation extends the definition of Born effective charges from insulators to conducting systems and relates them to a seemingly unrelated fundamental property of metals: the Drude weight. The second case I will discuss is the coupling of magnetism and phonons in materials. Specifically, I will demonstrate a DFT-based methodology for including the velocity-dependence of interatomic forces, which explicitly accounts for time-reversal symmetry breaking in the nuclear equations of motion. I will show that in some magnetic materials, such as CrI3, the assumption of adiabatic separation between electron and nuclear dynamics breaks down completely due to the role of (slow) spin dynamics in the coupling between phonons and the magnetic order.

Dr. Romain Vasseur, University of Massachusetts  Amherst

Learning global charges from local measurements

Monitored random quantum circuits (MRCs) exhibit a measurement-induced phase transition between area-law and volume-law entanglement scaling. In this talk, I will review the physics of such entanglement transitions, and discuss the current status of this field as well as recent experimental realizations. I will argue that MRCs with a conserved charge additionally exhibit two distinct volume-law entangled phases that cannot be characterized by equilibrium notions of symmetry-breaking or topological order, but rather by the non-equilibrium dynamics and steady-state distribution of charge fluctuations. These include a charge-fuzzy phase in which charge information is rapidly scrambled leading to slowly decaying spatial fluctuations of charge in the steady state, and a charge-sharp phase in which measurements collapse quantum fluctuations of charge without destroying the volume-law entanglement of neutral degrees of freedom. I will present some statistical mechanics description of such charge-sharpening transitions, and relate them to the efficiency of classical decoders to “learn” the global charge of quantum systems from local measurements.

Dr. Abhishek Bannerjee, Harvard University

Prof. Chris Laumann, Boston University

Condensed-matter systems provide alternative “vacua” exhibiting emergent low-energy properties dramatically different from those of the standard model. A case in point is the emergent quantum electrodynamics (QED) in the family of magnetic materials known as quantum spin ice. The emergent QED possesses many features familiar from our universe, such as charges, anti-charges and photons, but also
many unfamiliar one, such as magnetic monopoles. Thus these magnetic insulators provide a laboratory for exploring effective QED in regimes quite inaccessible to traditional Maxwell electromagnetism.

In this talk, I will review the beautiful picture of how QED emerges in these frustrated magnets when quantum fluctuations cause the spins to fractionalize into spinons – and what this has to do with ice and pyrochlore materials. We will then turn to several results regarding its fine structure. We will see that the fine structure constant – the dimensionless coupling which controls the interactions between
emergent light and charges – generically takes values ~0.1 in quantum spin ice, much larger than the \(\alpha\) ~ 1/137 of our universe [1]. This leads to a variety of predictions regarding the coherent dynamics of the spinons which we expect can be probed by neutron scattering [2]. Finally, we will consider how true electric fields couple into this magnetic insulator – and may permit the indirect observation of
the emergent magnetic monopole and a curious inverted Lorentz force [3].

[1] Pace, Morampudi, Moessner, Laumann. Phys. Rev. Lett. 127, 117205 (2021).
[2] Morampudi, Wilczek, Laumann. Phys. Rev. Lett. 124, 097204 (2020).
[3] Laumann, Moessner. arXiv:2302.06635.

Dr. Oleg Gorobtsov, Cornell University

In quantum materials, coexistent degrees of freedom such as spin, charge, and lattice respond in concert to various external stimuli including light and electrical current. Understanding the interactions between these degrees of freedom and stimuli promises advances in technology from next-generation electronics to energy storage. From coexistent emergent phases and far-from-equilibrium states to topological defects and nanomaterial morphology, nanostructural heterogeneities in space and time connected to crystal lattice commonly underpin the material behavior. Breakthrough coherent X-ray scattering techniques at novel X-ray sources capture nanoscale changes in lattice in-situ to connect them to macroscopic properties. Precise control over lattice dynamics by photoexcitations on sub-picosecond timescales sheds light on interaction between lattice dynamics and electronic order in chromium, an archetypal density wave material. In Mott insulators, nanoscale measurements reveal novel hierarchy and transition behavior of heterogeneities during metal-insulator transitions. Unique capabilities of coherent X-ray science offer us glimpses into the physics of phase transition in quantum materials and future design possibilities.