DODuncan H J O'DEll

Duncan H J O'DEll

McMaster University
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Duncan H J O'DEll has a total of 75 co-authors. Here are the top co-authors by number of shared publications:

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    A Maxwell fish-eye lens in a Bose-Einstein condensate

    by Jelte Duchene, Elinor Kath, Floriane Arrouas, Hanyi Jang, Helmut Strobel, Markus Oberthaler, Jay Mehta, Liam M. Farrell, Wyatt Kirkby, Duncan H J O'DEll

    We experimentally realize an analogue of the optical Maxwell fish-eye lens (MFEL) using phononic excitations in a Bose–Einstein condensate (BEC). A MFEL is characterized by a radially symmetric, spatially varying refractive index with the remarkable property that rays emitted from any point within the lens are perfectly focused at their antipodal points. While the implementation of such gradient-index lenses is challenging in conventional optical systems, BECs offer a highly tunable platform in which the spatially varying speed of sound of collective excitations -- phonons, the acoustic analogues of photons -- can be engineered and their dynamics observed in real time. Time-resolved measurements of phonon wavefronts reveal focusing behavior that shows good agreement with analytical theory and numerical simulations. This work provides both a geometric and physical framework for engineering effective refractive indices using ultracold atoms, and simulating wave propagation on effective spherical geometries.

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    Universal scaling of quantum caustics in the dynamics of interacting particles

    by Monalisa Singh Roy, Jesse Mumford, Amit Ozer, Oded Porat, D. H. J. O'DEll, Emanuele G. Dalla Torre

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    Topologically protected Bell-cat states in a simple spin model

    by B. Lajci, D. H. J. O'DEll, J. Mumford

    Cited by 4
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    Gauge potentials and vortices in the Fock space of a pair of periodically driven Bose-Einstein condensates

    by J. Mumford, D. Kamp, D. H. J. O'DEll

    Cited by 3
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    Dynamical phase transitions, caustics, and quantum dark bands

    by Valentin Link, Walter T Strunz, D H J O’dEll

    We provide a new perspective on quantum dynamical phase transitions (DPTs) by explaining their origin in terms of caustics that form in the Fock space representation of the many-body state over time, using the fully connected transverse field Ising model as an example. In this way we establish a connection between DPTs in a quantum spin system and an everyday natural phenomenon: The dark band between the primary and secondary bows (caustics) in rainbows known as Alexander’s dark band. The DPT occurs when the Loschmidt echo crosses the switching line between the evanescent tails of two back-to-back Airy functions that dress neighbouring fold caustics in Fock space and is the time-dependent analogue of what is seen as a function of angle in the sky. The structural stability and universal properties of caustics, as described mathematically by catastrophe theory, explains the generic occurrence of DPTs in the model and suggests that our analysis has wide applicability. Based on our thorough analytical understanding we propose a protocol which can be used to verify the existence of a DPT in a finite system experiment.

    Cited by 1
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    Duality between the quantum inverted harmonic oscillator and inverse square potentials

    by Sriram Sundaram, C P Burgess, D H J O’dEll

    In this paper we show how the quantum mechanics of the inverted harmonic oscillator (IHO) can be mapped to the quantum mechanics of a particle in a super-critical inverse square potential (ISP). We demonstrate this by relating both of these systems to the Berry–Keating system with Hamiltonian H = ( x p + p x ) / 2 . It has long been appreciated that the quantum mechanics of the ISP has an ambiguity in choosing a boundary condition near the origin and we show how this ambiguity is mapped to the IHO system. Imposing a boundary condition requires specifying a distance scale where it is applied and changes to this scale come with a renormalisation group (RG) evolution of the boundary condition that ensures observables do not directly depend on the scale (which is arbitrary). Physical scales instead emerge as RG invariants of this evolution. The RG flow for the ISP is known to follow limit cycles describing the discrete breaking of classical scale invariance in a simple example of a quantum anomaly, and we find that limit cycles also occur for the IHO. However, unlike the ISP where the continuous scaling symmetry is explicit, in the case of the IHO it is hidden and occurs because the Hamiltonian is part of a larger su(1,1) spectrum generating algebra. Our map does not require the boundary condition to be self-adjoint, as can be appropriate for systems that involve the absorption or emission of particles.

    Cited by 17
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    Duality between the quantum inverted harmonic oscillator and inverse square potentials

    by Sriram Sundaram, C. P. Burgess, D. H. J. O'Dell

    In this paper we show how the quantum mechanics of the inverted harmonic oscillator can be mapped to the quantum mechanics of a particle in a super-critical inverse square potential. We demonstrate this by relating both of these systems to the Berry-Keating system with hamiltonian $H=(xp+px)/2$. It has long been appreciated that the quantum mechanics of the inverse square potential has an ambiguity in choosing a boundary condition near the origin and we show how this ambiguity is mapped to the inverted harmonic oscillator system. Imposing a boundary condition requires specifying a distance scale where it is applied and changes to this scale come with a renormalization group (RG) evolution of the boundary condition that ensures observables do not directly depend on the scale (which is arbitrary). Physical scales instead emerge as RG invariants of this evolution. The RG flow for the inverse square potential is known to follow limit cycles describing the discrete breaking of classical scale invariance in a simple example of a quantum anomaly, and we find that limit cycles also occur for the inverted harmonic oscillator. However, unlike the inverse square potential where the continuous scaling symmetry is explicit, in the case of the inverted harmonic oscillator it is hidden and occurs because the hamiltonian is part of a larger su(1,1) spectrum generating algebra. Our map does not require the boundary condition to be self-adjoint, as can be appropriate for systems that involve the absorption or emission of particles.

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    Scaling at the out-of-time-ordered correlator wavefront: Free versus chaotic models

    by Jonathon Riddell, Wyatt Kirkby, D. H. J. O'Dell, Erik S. Sørensen

    Out-of-time-ordered correlators (OTOCs) are useful tools for investigating foundational questions such as thermalization in closed quantum systems because they can potentially distinguish between integrable and nonintegrable dynamics. Here, we discuss the properties of wavefronts of OTOCs by focusing on the region around the main wavefront at x=vBt, where vB is the butterfly velocity. Using a Heisenberg spin model as an example, we find that the leading edge of a propagating Gaussian with the argument −m(x)(x−vBt)2+b(x)t gives an excellent fit to the region around x=vBt for both the free and chaotic cases. However, the scaling in these two regimes is very different: in the free case the coefficients m(x) and b(x) have an inverse power law dependence on x, whereas in the chaotic case they decay exponentially. We conjecture that this result is universal by using catastrophe theory to show that, on the one hand, the wavefront in the free case has to take the form of an Airy function and its local expansion shows that the power law scaling seen in the numerics holds rigorously and, on the other hand, an exponential scaling of the OTOC wavefront must be a signature of nonintegrable dynamics. We find that the crossover between the two regimes is smooth and characterized by an S-shaped curve giving the lifting of Airy nodes as a function of a chaos parameter. This shows that the Airy form is qualitatively stable against weak chaos and consistent with the concept of a quantum Kolmogorov-Arnold-Moser theory.

    Cited by 17
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    Scaling at the OTOC Wavefront: free versus chaotic models

    by Jonathon Riddell, Wyatt Kirkby, D. H. J. O'Dell, Erik S. Sørensen

    Out of time ordered correlators (OTOCs) are useful tools for investigating foundational questions such as thermalization in closed quantum systems because they can potentially distinguish between integrable and nonintegrable dynamics. Here we discuss the properties of wavefronts of OTOCs by focusing on the region around the main wavefront at $x=v_{B}t$, where $v_{B}$ is the butterfly velocity. Using a Heisenberg spin model as an example, we find that the leading edge of a propagating Gaussian with the argument $-m(x)\left( x-v_B t \right)^2 +b(x)t$ gives an excellent fit to the region around $x=v_{B}t$ for both the free and chaotic cases. However, the scaling in these two regimes is very different: in the free case the coefficients $m(x)$ and $b(x)$ have an inverse power law dependence on $x$ whereas in the chaotic case they decay exponentially. We conjecture that this result is universal by using catastrophe theory to show that, on the one hand, the wavefront in the free case has to take the form of an Airy function and its local expansion shows that the power law scaling seen in the numerics holds rigorously, and on the other hand an exponential scaling of the OTOC wavefront must be a signature of nonintegrable dynamics. We find that the crossover between the two regimes is smooth and characterized by an S-shaped curve giving the lifting of Airy nodes as a function of a chaos parameter. This shows that the Airy form is qualitatively stable against weak chaos and consistent with the concept of a quantum Kolmogorov-Arnold-Moser theory.

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    Caustics in the sine-Gordon model from quenches in coupled one-dimensional Bose gases

    by Aman Agarwal, Manas Kulkarni, D. H. J. O'DEll

    Caustics are singularities that occur naturally in optical, hydrodynamic, and quantum waves, giving rise to high-amplitude patterns that can be described using catastrophe theory. In this paper we study caustics in a statistical field theory setting in the form of the sine-Gordon model that describes a variety of physical systems including coupled one-dimensional (1D) superfluids. Specifically, we use classical field simulations to study the dynamics of two ultracold 1D Bose gases (quasicondensates) that are suddenly coupled to each other and find that the resulting nonequilibrium dynamics is dominated by caustics. Thermal noise is included by sampling the initial states from a Boltzmann distribution for phononic excitations. We find that caustics pile up over time in both the number and phase difference observables, leading to a characteristic nonthermal circus-tent-shaped probability distribution at long times.

    Cited by 2
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