Preprints

1. Jr., F. A. B., Dziarmaga, J., Rams, M. M., & Zurek, W. H. (2024). Persistent coherent many-body oscillations in a non-integrable quantum Ising chain.
   ARXIV BIB ABSTRACT

   @unpublished{bayocboc2024persistentcoherentmanybodyoscillations,
     title = {Persistent coherent many-body oscillations in a non-integrable quantum Ising chain},
     author = {Jr., Francis A. Bayocboc and Dziarmaga, Jacek and Rams, Marek M. and Zurek, Wojciech H.},
     year = {2024},
     eprint = {2407.06036},
     archiveprefix = {arXiv},
     primaryclass = {quant-ph},
     doi = {2407.06036}
   }
   

   We identify persistent oscillations in a nonintegrable quantum Ising chain left behind by a rapid transition into a ferromagnetic phase. In the integrable chain with nearest-neighbor (NN) interactions, the nature, origin, and decay of post-transition oscillations are tied to the Kibble-Zurek mechanism (KZM). However, when coupling to the next nearest neighbor (NNN) is added, the resulting nonintegrable Ising chain (still in the quantum Ising chain universality class) supports persistent post-transition oscillation: KZM-like oscillations turn into persistent oscillations of transverse magnetization. Their longevity in our simulations is likely limited only by the numerical accuracy. Their period differs from the decaying KZM oscillation but their amplitude depends on quench rate. Moreover, they can be excited by driving in resonance with the excitations’ energy gap. Thus, while one might have expected that the integrability-breaking NNN coupling would facilitate relaxation, the oscillations we identify are persistent. At low to medium transverse fields, they are associated with Cooper pairs of Bogoliubov quasiparticles – kinks. This oscillation of the pair condensate is a manifestation of quantum coherence. 

Refereed journal articles

1. Sokolov, I., Bayocboc, F. A., Rams, M. M., & Dziarmaga, J. (2024). Inhomogeneous adiabatic preparation of a quantum critical ground state in two dimensions. Phys. Rev. B, 110(5), 054410.
   PDF DOI BIB ABSTRACT

   @article{sokolov2024InhomogeneousAdiabaticPreparation,
     title = {Inhomogeneous adiabatic preparation of a quantum critical ground state in two dimensions},
     author = {Sokolov, Ihor and Bayocboc, Francis A. and Rams, Marek M. and Dziarmaga, Jacek},
     journal = {Phys. Rev. B},
     volume = {110},
     issue = {5},
     pages = {054410},
     numpages = {12},
     year = {2024},
     month = aug,
     publisher = {American Physical Society},
     doi = {10.1103/PhysRevB.110.054410},
     file = {PhysRevB.110.054410.pdf}
   }
   

   Adiabatic preparation of a critical ground state is hampered by the closing of its energy gap as the system size increases. However, this gap is directly relevant only for a uniform ramp, where a control parameter in the Hamiltonian is tuned uniformly in space towards the quantum critical point. Here, we consider inhomogeneous ramps in two dimensions: initially, the parameter is made critical at the center of a lattice, from where the critical region expands at a fixed velocity. In the 1D and 2D quantum Ising models, which have a well-defined speed of sound at the critical point, the ramp becomes adiabatic with a subsonic velocity. This subsonic ramp can prepare the critical state faster than a uniform one. Moreover, in both a model of p-wave paired 2D fermions and the Kitaev model, the critical dispersion is anisotropic—linear with a nonzero velocity in one direction and quadratic in the other—but the gap is still inversely proportional to the linear size of the critical region, with a coefficient proportional to the nonzero velocity. This suffices to make the inhomogeneous ramp adiabatic below a finite crossover velocity and superior to the homogeneous one.

2. Bayocboc, F. A., Dziarmaga, J., & Zurek, W. H. (2024). Biased dynamics of the miscible-immiscible quantum phase transition in a binary Bose-Einstein condensate. Phys. Rev. B, 109(6), 064501.
   PDF DOI BIB ABSTRACT

   @article{bayocboc2024BiasedDynamics,
     title = {Biased dynamics of the miscible-immiscible quantum phase transition in a binary Bose-Einstein condensate},
     author = {Bayocboc, Francis A. and Dziarmaga, Jacek and Zurek, Wojciech H.},
     journal = {Phys. Rev. B},
     volume = {109},
     issue = {6},
     pages = {064501},
     numpages = {11},
     year = {2024},
     month = feb,
     publisher = {American Physical Society},
     doi = {10.1103/PhysRevB.109.064501},
     file = {PhysRevB.109.064501.pdf}
   }
   

   A quantum phase transition from the miscible to the immiscible phase of a quasi-one-dimensional binary Bose-Einstein condensate is driven by ramping down the coupling amplitude of its two hyperfine states. It results in a random pattern of spatial domains where the symmetry is broken separated by defects. In distinction to previous studies [J. Sabbatini et al., Phys. Rev. Lett. 107, 230402 (2011), New J. Phys. 14 095030 (2012)], we include nonzero detuning between the light field and the energy difference of the states, which provides a bias towards one of the states. Using the truncated Wigner method, we test the biased version of the quantum Kibble-Zurek mechanism [M. Rams et al., Phys. Rev. Lett. 123, 130603 (2019)] and observe a crossover to the adiabatic regime when the quench is sufficiently fast to dominate the effect of the bias. We verify a universal power law for the population imbalance in the nonadiabatic regime both at the critical point and by the end of the ramp. Shrinking and annihilation of domains of the unfavourable phase after the ramp, that is, already in the broken symmetry phase, enlarges the defect-free sections by the end of the ramp. The consequences of this phase-ordering effect can be captured by a phenomenological power law. 

3. Francis A. Bayocboc, J., & Kheruntsyan, K. V. (2023). Frequency beating and damping of breathing oscillations of a harmonically trapped one-dimensional quasicondensate. Comptes Rendus. Physique, 24(S3), 15–38.
   PDF DOI BIB ABSTRACT

   @article{bayocboc2023,
     author = {Francis A. Bayocboc, Jr. and Kheruntsyan, Karen V.},
     title = {Frequency beating and damping of breathing oscillations of a harmonically trapped one-dimensional quasicondensate},
     journal = {Comptes Rendus. Physique},
     pages = {15--38},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {24},
     number = {S3},
     year = {2023},
     doi = {10.5802/crphys.131},
     language = {en},
     file = {CRPHYS_2023__24_S3_15_0.pdf}
   }
   

   We study the breathing (monopole) oscillations and their damping in a harmonically trapped one-dimensional (1D) Bose gas in the quasicondensate regime using a finite-temperature classical field approach. By characterising the oscillations via the dynamics of the density profile’s rms width over long time, we find that the rms width displays beating of two distinct frequencies. This means that the 1D Bose gas oscillates not at a single breathing mode frequency, as found in previous studies, but as a superposition of two distinct breathing modes, one oscillating at frequency close to ≃\sqrt3ωand the other at ≃2ω, where ωis the trapping frequency. The breathing mode at ≃\sqrt3ωdominates the beating at lower temperatures, deep in the quasicondensate regime, and can be attributed to the oscillations of the bulk of the density distribution comprised of particles populating low-energy, highly-occupied states. The breathing mode at ≃2ω, on the other hand, dominates the beating at higher temperatures, close to the nearly ideal, degenerate Bose gas regime, and is attributed to the oscillations of the tails of the density distribution comprised of thermal particles in higher energy states. The two breathing modes have distinct damping rates, with the damping rate of the bulk component being approximately four times larger than that of the tails component.

4. Bayocboc, F. A., Davis, M. J., & Kheruntsyan, K. V. (2022). Dynamics of thermalization of two tunnel-coupled one-dimensional quasicondensates. Phys. Rev. A, 106(2), 023320.
   PDF DOI BIB ABSTRACT

   @article{bayocboc2022,
     title = {Dynamics of thermalization of two tunnel-coupled one-dimensional quasicondensates},
     author = {Bayocboc, F. A. and Davis, M. J. and Kheruntsyan, K. V.},
     journal = {Phys. Rev. A},
     volume = {106},
     issue = {2},
     pages = {023320},
     numpages = {14},
     year = {2022},
     month = aug,
     publisher = {American Physical Society},
     doi = {10.1103/PhysRevA.106.023320},
     file = {PhysRevA.106.023320.pdf}
   }
   

   We study the nonequilibrium dynamics of two tunnel-coupled one-dimensional quasicondensates following a quench of the coupling strength from zero to a fixed finite value. More specifically, starting from two independent quasicondensates in thermal equilibrium, with initial temperature and chemical potential imbalance, we suddenly switch on the tunnel-coupling and analyze the postquench equilibration in terms of particle number and energy imbalances. We find that, in certain parameter regimes, the net energy can flow from the colder quasicondensate to the hotter one and is governed by the surplus of low-energy particles flowing from the cold to the hot system relative to the high-energy particles flowing in the reverse direction. In all cases, the approach to the new thermal equilibrium occurs through transient, damped oscillations. We also find that, for a balanced initial state, the coupled quasicondensates can relax into a final thermal equilibrium state in which they display a thermal phase coherence length that is larger than their initial phase coherence length, even though the new equilibrium temperature is higher. The increase in the phase coherence length occurs due to phase locking which manifests itself via an increased degree of correlation between the local relative phases of the quasicondensates at two arbitrary points.

5. Simmons, S. A., Bayocboc, F. A., Pillay, J. C., Colas, D., McCulloch, I. P., & Kheruntsyan, K. V. (2020). What is a Quantum Shock Wave? Phys. Rev. Lett., 125(18), 180401.
   PDF DOI BIB ABSTRACT

   @article{simmons2020QuantumShockWave,
     title = {What is a Quantum Shock Wave?},
     author = {Simmons, S. A. and Bayocboc, F. A. and Pillay, J. C. and Colas, D. and McCulloch, I. P. and Kheruntsyan, K. V.},
     journal = {Phys. Rev. Lett.},
     volume = {125},
     issue = {18},
     pages = {180401},
     numpages = {6},
     year = {2020},
     month = oct,
     publisher = {American Physical Society},
     doi = {10.1103/PhysRevLett.125.180401},
     file = {PhysRevLett.125.180401.pdf}
   }
   

   Shock waves are examples of the far-from-equilibrium behavior of matter; they are ubiquitous in nature, yet the underlying microscopic mechanisms behind their formation are not well understood. Here, we study the dynamics of dispersive quantum shock waves in a one-dimensional Bose gas, and show that the oscillatory train forming from a local density bump expanding into a uniform background is a result of quantum mechanical self-interference. The amplitude of oscillations, i.e., the interference contrast, decreases with the increase of both the temperature of the gas and the interaction strength due to the reduced phase coherence length. Furthermore, we show that vacuum and thermal fluctuations can significantly wash out the interference contrast, seen in the mean-field approaches, due to shot-to-shot fluctuations in the position of interference fringes around the mean.

6. Cuansing, E. C., Bayocboc, F. A., & Laurio, C. M. (2017). Dynamics of electron currents in nanojunctions with time-varying components and interactions. AIP Conference Proceedings, 1871(1), 030003.
   PDF DOI BIB ABSTRACT

   @article{cuansing2017,
     author = {Cuansing, Eduardo C. and Bayocboc, Francis A. and Laurio, Christian M.},
     title = {{Dynamics of electron currents in nanojunctions with time-varying components and interactions}},
     journal = {AIP Conference Proceedings},
     volume = {1871},
     number = {1},
     pages = {030003},
     year = {2017},
     month = aug,
     issn = {0094-243X},
     doi = {10.1063/1.4996522},
     eprint = {https://pubs.aip.org/aip/acp/article-pdf/doi/10.1063/1.4996522/13751464/030003\_1\_online.pdf},
     file = {030003_1_online.pdf}
   }
   

   We study the dynamics of the electron current in nanodevices where there are time-varying components and interactions. These devices are a nanojunction attached to heat baths and with dynamical electron-phonon interactions, and a nanojunction with photon beams incident and reflected at the channel. We use the two-time nonequilibrium Green’s functions technique to calculate the time-dependent electron current flowing across the devices. We find that whenever a sudden change occurs in the device, the current takes time to react to the abrupt change, overshoots, oscillates, and eventually settles down to a steady value. With dynamical electron-phonon interactions, the interaction gives rise to a net resistance that reduces the flow of current across the device when a source-drain bias potential is attached. In the presence of dynamical electron-photon interactions, the photons drive the electrons to flow. The direction of flow, however, depends on the frequencies of the incident photons. Furthermore, the direction of electron flow in one lead is exactly opposite to the direction of flow in the other lead thereby resulting in no net change in current flowing across the device.

7. Bayocboc, F. A., & Paraan, F. N. C. (2015). Exact work statistics of quantum quenches in the anisotropic XY model. Phys. Rev. E, 92(3), 032142.
   PDF DOI BIB ABSTRACT

   @article{bayocboc2015,
     title = {Exact work statistics of quantum quenches in the anisotropic $XY$ model},
     author = {Bayocboc, Francis A. and Paraan, Francis N. C.},
     journal = {Phys. Rev. E},
     volume = {92},
     issue = {3},
     pages = {032142},
     numpages = {9},
     year = {2015},
     month = sep,
     publisher = {American Physical Society},
     doi = {10.1103/PhysRevE.92.032142},
     file = {PhysRevE.92.032142.pdf}
   }
   

   We derive exact analytic expressions for the average work done and work fluctuations in instantaneous quenches of the ground and thermal states of a one-dimensional anisotropic XY model. The average work and a quantum fluctuation relation is used to determine the amount of irreversible entropy produced during the quench, eventually revealing how the closing of the excitation gap leads to increased dissipated work. The work fluctuation is calculated and shown to exhibit nonanalytic behavior as the prequench anisotropy parameter and transverse field are tuned across quantum critical points. Exact compact formulas for the average work and work fluctuation in ground state quenches of the transverse field Ising model allow us to calculate the first singular field derivative at the critical field values.

Refereed conference proceedings

Theses

1. Bayocboc Jr, F. A. (2021). Quench dynamics and relaxation of one-dimensional Bose gases [PhD thesis]. The University of Queensland; Available at \urlhttps://doi.org/10.14264/4222d2d.
   DOI ABSTRACT

   @phdthesis{bayocboc2021quench,
     title = {Quench dynamics and relaxation of one-dimensional Bose gases},
     author = {Bayocboc Jr, Francis A},
     year = {2021},
     doi = {10.14264/4222d2d},
     note = {Available at \url{https://doi.org/10.14264/4222d2d}},
     school = {The University of Queensland},
     type = {PhD thesis}
   }
   

   Ultracold atom experiments are a great experimental platform for studying many-body physics due to their isolation and high tunability. In particular, they are excellent candidates for studying many paradigmatic models of quantum many-body physics with a high degree of accuracy. Advances in ultracold atom experiments have enabled the realisation of lower-dimensional systems that have been of theoretical interest historically. Low dimensional systems have several striking differences from their three-dimensional counterparts; most notable is the absence of Bose-Einstein condensation in the thermodynamic limit. In this thesis, we study the nonequilibrium dynamics of quantum many-body interacting ultracold Bose gases. We are particularly interested in quenches of Bose gases in one spatial dimension and their subsequent time-evolution and relaxation dynamics. We present numerical simulations of one-dimensional Bose gases where we incorporate thermal and quantum fluctuations and investigate their effects on the post-quench dynamics of the system.
   
   First, we consider a system of two tunnel-coupled, one-dimensional quasicondensates following a quench of the coupling strength from zero to a fixed finite value. More specifically, starting from two independent quasicondensates in equilibrium, with an initial temperature and chemical potential imbalance, we suddenly switch on the tunnel-coupling and analyse the post-quench equilibration dynamics. We find that after coupling the quasicondensates, the low-energy particles flow predominantly from the colder quasicondensate to the hotter one, whereas the reverse is true for the higher-energy particles. The net energy flow is governed by the surplus (or otherwise) of the overall number of lower energy particles flowing from the initially colder quasicondensate to the initially hotter quasicondensate, compared to the overall number of higher-energy particles flowing in the opposite direction. We also find that the coupled quasicondensates can evolve to a relaxed state with a higher equilibrium temperature than their initial temperature. Surprisingly, we find that, though the final equilibrium temperature is higher, the system can have a higher phase coherence within each quasicondensate.
   
   We also consider the case where the two quasicondensates in the system above contain an equal number of particles with an initial phase difference. The two quasicondensates are obtained from the coherent splitting of a single quasicondensate. After imprinting an initial phase difference, we abruptly turn on the coupling strength between the two and characterise the post-quench dynamics. This is motivated by a recent experiment of Pigneur et al., Phys. Rev. Lett. 120, 173601 (2018), where the fast relaxation of the system to a phase-locked state cannot be described by the quantum sine-Gordon model that has described their experimental results well in the past. We find that our 1D simulations of the experiment can reproduce the phase-locked steady state but not the fast decay observed in the experiment.
   
   We then investigate the breathing mode oscillations of a one-dimensional Bose gas after a quench of the longitudinal harmonic trap frequency. In particular, after preparing a Bose gas at a chemical potential and temperature, we suddenly change the longitudinal trapping frequency to a lower value and observe the dynamics of the gas. We find that two breathing modes corresponding to two components of the system exist: low-energy particles occupying the bulk and high-energy particles in the tails of the Bose gas. Each component has its own distinct breathing frequency and damping rate. We find that the low-energy particles in the bulk have dynamical behaviour closer to that of a zero temperature quasicondensate, whereas highly energetic particles in the tails have dynamical behaviour closer to that of an ideal Bose gas. We also find that the damping rate of the quasicondensate is much lower than the rate predicted from one-dimensional Landau damping.
   
   Lastly, we consider the effects of thermal and quantum fluctuations on the dynamics of dispersive quantum shock waves in a one-dimensional Bose gas. Starting with a local density bump on top of a uniform background density, we let the former expand into the latter and observe the formation and dynamics of dispersive shock waves. Here, the oscillatory train that forms after releasing the local density bump results from quantum mechanical self-interference. We find that the amplitude of oscillation decreases with the increase of temperature due to the reduced phase coherence within the Bose gas. Furthermore, we find that vacuum and thermal fluctuations can significantly wash out the amplitude of oscillations due to shot-to-shot fluctuations in the position of interference fringes around the mean.

2. Bayocboc Jr, F. A. (2015). Work fluctuation and irreversible entropy in a quenched XY Heisenberg magnet [MSc thesis]. University of the Philippines, Diliman.
   PDF ABSTRACT

   @mastersthesis{bayocboc2015XYquench,
     title = {Work fluctuation and irreversible entropy in a quenched XY Heisenberg magnet},
     author = {Bayocboc Jr, Francis A},
     year = {2015},
     school = {University of the Philippines, Diliman},
     type = {MSc thesis},
     file = {bayocboc2015XYquench_MSthesis.pdf}
   }
   

   In this thesis, we study the emergent thermodynamics associated with an arbitrary quench in the Heisenberg XY model by calculating the work fluctuation and the irreversible entropy produced. For the fluctuation in the work done, an exact expression is obtained and is shown to exhibit non-analytic behavior as the pre-quench transverse field and anisotropy parameter cross quantum critical points. On the other hand, the irreversible entropy is obtained by calculating the difference between the average work done and an effective free energy change. We emphasize on the effect of the anisotropy parameter on the irreversible entropy, adding to previous works done on the Transverse Field Ising Model.