DPhil (Oxon)

Title: Competition between Weak Quantum Measurement and Many-Body Dynamics in Ultracold Bosonic Gases

Supervisor: Dr. Igor B. Mekhov

Abstract: Trapping ultracold atoms in optical lattices enabled the study of strongly correlated phenomena in an environment that is far more controllable and tunable than what was possible in condensed matter. Here, we consider coupling these systems to quantised light where the quantum nature of both the optical and matter fields play equally important roles in order to push the boundaries of what is possible in ultracold atomic systems.

We show that light can serve as a nondestructive probe of the quantum state of matter. By considering a global measurement we show that it is possible to distinguish a highly delocalised phase like a superfluid from the Bose glass and Mott insulator. We also demonstrate that light scattering reveals not only density correlations, but also matter-field interference.

By taking into account the effect of measurement backaction we show that the measurement can efficiently compete with the local atomic dynamics of the quantum gas. This can generate long-range correlations and entanglement which in turn leads to macroscopic multimode oscillations across the whole lattice when the measurement is weak and correlated tunnelling, as well as selective suppression and enhancement of dynamical processes beyond the projective limit of the quantum Zeno effect in the strong measurement regime.

We also consider quantum measurement backaction due to the measurement of matter-phase-related variables such as global phase coherence. We show how this unconventional approach opens up new opportunities to affect system evolution and demonstrate how this can lead to a new class of measurement projections thus extending the measurement postulate for the case of strong competition with the system’s own evolution.

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MSci (Cantab)

Title: Theoretical and Numerical Study of Models of Entanglement for Neutrons

Supervisor: Prof. Crispin H. W. Barnes

Abstract: We propose and investigate a scheme for detecting gravitational waves using the entanglement generated by the dynamics of a pair of neutrons trapped in a harmonic well. We develop a model that combines the effects due to plane gravitational wave solutions of the linearised field equations in the weak-field limit of general relativity with the time-dependent Schrödinger equation. Numerical simulations show that entanglement amplifies the effect of high frequency gravitational waves on the quantum state. In the proposed experiment, for realistic wave amplitudes and frequencies, the final state is practically indistinguishable from one unaffected by gravitational radiation. However, the results also show that quantum entanglement could be used in the future for high frequency gravitational wave detection.

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Title: Quantum State Reduction by Matter-Phase-Related Measurements in Optical Lattices

Authors: Wojciech Kozlowski, Santiago F. Caballero-Benitez, Igor B. Mekhov

Abstract: A many-body atomic system coupled to quantized light is subject to weak measurement. Instead of coupling light to the on-site density, we consider the quantum backaction due to the measurement of matter-phase-related variables such as global phase coherence. We show how this unconventional approach opens up new opportunities to affect system evolution. We demonstrate how this can lead to a new class of final states different from those possible with dissipative state preparation or conventional projective measurements. These states are characterised by a combination of Hamiltonian and measurement properties thus extending the measurement postulate for the case of strong competition with the system’s own evolution.

Journal Reference: Scientific Reports 7, Article number: 42597 (2017)

Full Text: Scientific Reports - arXiv


Title: Collective dynamics of multimode bosonic systems induced by weak quantum measurement

Authors: Gabriel Mazzucchi, Wojciech Kozlowski, Santiago F. Caballero-Benitez, Igor B. Mekhov

Abstract: In contrast to the fully projective limit of strong quantum measurement, where the evolution is locked to a small subspace (quantum Zeno dynamics), or even frozen completely (quantum Zeno effect), the weak non-projective measurement can effectively compete with standard unitary dynamics leading to nontrivial effects. Here we consider global weak measurement addressing collective variables, thus preserving quantum superpositions due to the lack of which path information. While for certainty we focus on ultracold atoms, the idea can be generalized to other multimode quantum systems, including various quantum emitters, optomechanical arrays, and purely photonic systems with multiple-path interferometers (photonic circuits). We show that light scattering from ultracold bosons in optical lattices can be used for defining macroscopically occupied spatial modes that exhibit long-range coherent dynamics. Even if the measurement strength remains constant, the quantum measurement backaction acts on the atomic ensemble quasi-periodically and induces collective oscillatory dynamics of all the atoms. We introduce an effective model for the evolution of the spatial modes and present an analytic solution showing that the quantum jumps drive the system away from its stable point. We confirm our finding describing the atomic observables in terms of stochastic differential equations.

Journal Reference: New Journal of Physics, 18(7), 73017, 2016

Full Text: New Journal of Physics - arXiv


Title: Non-Hermitian Dynamics in the Quantum Zeno Limit

Authors: Wojciech Kozlowski, Santiago F. Caballero-Benitez, Igor B. Mekhov

Abstract: Measurement is one of the most counter-intuitive aspects of quantum physics. Frequent measurements of a quantum system lead to quantum Zeno dynamics where time evolution becomes confined to a subspace defined by the projections. However, weak measurement performed at a finite rate is also capable of locking the system into such a Zeno subspace in an unconventional way: by Raman-like transitions via virtual intermediate states outside this subspace, which are not forbidden. Here, we extend this concept into the realm of non-Hermitian dynamics by showing that the stochastic competition between measurement and a system's own dynamics can be described by a non-Hermitian Hamiltonian. We obtain an analytic solution for ultracold bosons in a lattice and show that a dark state of the tunnelling operator is a steady state in which the observable's fluctuations are zero and tunnelling is suppressed by destructive matter-wave interference. This opens a new venue of investigation beyond the canonical quantum Zeno dynamics and leads to a new paradigm of competition between global measurement backaction and short-range atomic dynamics.

Journal Reference: Phys. Rev. A 94, 012123 (2016)

Full Text: Physical Review A - arXiv


Title: Probing and Manipulating Fermionic and Bosonic Quantum Gases with Quantum Light

Authors: Thomas J. Elliott, Gabriel Mazzucchi, Wojciech Kozlowski, Santiago F. Caballero-Benitez, Igor B. Mekhov

Abstract: We study the atom-light interaction in the fully quantum regime, with focus on off-resonant light scattering into a cavity from ultracold atoms trapped in an optical lattice. The detection of photons allows the quantum nondemolition (QND) measurement of quantum correlations of the atomic ensemble, distinguishing between different quantum states. We analyse the entanglement between light and matter and show how it can be exploited for realising multimode macroscopic quantum superpositions such as Schrödinger cat states, for both bosons and fermions. We provide examples utilising different measurement schemes, and study their robustness to decoherence. Finally, we address the regime where the optical lattice potential is a quantum dynamical variable and is modified by the atomic state, leading to novel quantum phases, and significantly altering the phase diagram of the atomic system.

Journal Reference: Atoms 2015, 3(3), 392-406

Full Text: Atoms - arXiv


Title: Quantum Measurement-induced Dynamics of Many-Body Ultracold Bosonic and Fermionic Systems in Optical Lattices

Authors: Gabriel Mazzucchi*, Wojciech Kozlowski*, Santiago F. Caballero-Benitez, Thomas J. Elliott, Igor B. Mekhov
*equally contributing authors

Abstract: Trapping ultracold atoms in optical lattices enabled numerous breakthroughs uniting several disciplines. Coupling these systems to quantized light leads to a plethora of new phenomena and has opened up a new field of study. Here we introduce a physically novel source of competition in a many-body strongly correlated system: We prove that quantum backaction of global measurement is able to efficiently compete with intrinsic short-range dynamics of an atomic system. The competition becomes possible due to the ability to change the spatial profile of a global measurement at a microscopic scale comparable to the lattice period without the need of single site addressing. In coherence with a general physical concept, where new competitions typically lead to new phenomena, we demonstrate novel nontrivial dynamical effects such as large-scale multimode oscillations, long-range entanglement and correlated tunneling, as well as selective suppression and enhancement of dynamical processes beyond the projective limit of the quantum Zeno effect. We demonstrate both the break-up and protection of strongly interacting fermion pairs by measurement. Such a quantum optical approach introduces into many-body physics novel processes, objects, and methods of quantum engineering, including the design of many-body entangled environments for open systems.

Journal Reference: Phys. Rev. A 93, 023632 (2016)

Full Text: Physical Review A - arXiv


Title: Multipartite Entangled Spatial Modes of Ultracold Atoms Generated and Controlled by Quantum Measurement

Authors: Thomas J. Elliott, Wojciech Kozlowski, Santiago Caballero-Benitez, Igor B. Mekhov

Abstract: We show that the effect of measurement back-action results in the generation of multiple many-body spatial modes of ultracold atoms trapped in an optical lattice, when scattered light is detected. The multipartite mode entanglement properties and their nontrivial spatial overlap can be varied by tuning the optical geometry in a single setup. This can be used to engineer quantum states and dynamics of matter fields. We provide examples of multimode generalizations of parametric down-conversion, Dicke, and other states, investigate the entanglement properties of such states, and show how they can be transformed into a class of generalized squeezed states. Further, we propose how these modes can be used to detect and measure entanglement in quantum gases.

Journal Reference: Physical Review Letters 114, 113604 (2015)

Full Text: Physical Review Letters - arXiv


Title: Probing Matter-Field and Atom-Number Correlations in Optical Lattices by Global Nondestructive Addressing

Authors: Wojciech Kozlowski, Santiago F. Caballero-Benitez, Igor B. Mekhov

Abstract: We show that light scattering from an ultracold gas reveals not only density correlations, but also matter-field interference at its shortest possible distance in an optical lattice, which defines key properties such as tunneling and matter-field phase gradients. This signal can be enhanced by concentrating probe light between lattice sites rather than at density maxima. As addressing between two single sites is challenging, we focus on global nondestructive scattering, allowing probing order parameters, matter-field quadratures and their squeezing. The scattering angular distribution displays peaks even if classical diffraction is forbidden and we derive generalized Bragg conditions. Light scattering distinguishes all phases in the Mott insulator - superfluid - Bose glass phase transition.

Journal Reference: Physical Review A 92, 013613 (2015)

Full Text: Physical Review A - arXiv


Title: Buffering Capacity Explains Signal Variation in Symbiotic Calcium Oscillations

Authors: Emma Granqvist, Derin Wysham, Saul Hazledine, Wojciech Kozlowski, Jongho Sun, Myriam Charpentier, Teresa Vaz Martins, Pauline Haleux, Krasimira Tsaneva-Atanasova, J. Allan Downie, Giles E.D. Oldroyd, Richard J. Morris

Abstract: Legumes form symbioses with rhizobial bacteria and arbuscular mycorrhizal fungi that aid plant nutrition. A critical component in the establishment of these symbioses is nuclear-localized calcium (Ca2+) oscillations. Different components on the nuclear envelope have been identified as being required for the generation of the Ca2+ oscillations. Among these an ion channel, Doesn't Make Infections1, is preferentially localized on the inner nuclear envelope and a Ca2+ ATPase is localized on both the inner and outer nuclear envelopes. Doesn't Make Infections1 is conserved across plants and has a weak but broad similarity to bacterial potassium channels. A possible role for this cation channel could be hyperpolarization of the nuclear envelope to counterbalance the charge caused by the influx of Ca2+ into the nucleus. Ca2+ channels and Ca2+ pumps are needed for the release and reuptake of Ca2+ from the internal store, which is hypothesized to be the nuclear envelope lumen and endoplasmic reticulum, but the release mechanism of Ca2+ remains to be identified and characterized. Here, we develop a mathematical model based on these components to describe the observed symbiotic Ca2+ oscillations. This model can recapitulate Ca2+ oscillations, and with the inclusion of Ca2+-binding proteins it offers a simple explanation for several previously unexplained phenomena. These include long periods of frequency variation, changes in spike shape, and the initiation and termination of oscillations. The model also predicts that an increase in buffering capacity in the nucleoplasm would cause a period of rapid oscillations. This phenomenon was observed experimentally by adding more of the inducing signal.

Journal Reference: Plant physiology 160.4 (2012): 2300-2310

Full Text: Plant Physiology