:og:description: Papers co-authored by Nikola Šibalić, with accessible summaries.
.. meta::
:description: Papers co-authored by Nikola Šibalić, with accessible summaries.
:keywords: research papers, research topics
Research
========
Non-equilibrium phase transitions
---------------------------------
.. image:: _static/many_body.png
:width: 350
:align: right
Rydberg atoms driven with the laser fields, dissipating through spontaneous
emission and forced decay channels, with interactions tunable with static and
microwave/terahertz EM fields present ideal platform for exploration of
non-equilibrium dynamics in well-controlable way. We recently explored
numerically non-equilibrium phase diagrams of these systems, and found that
phase diagrams depend qualitatively on the cross-over range between short-range
(van der Waals) and long-range (resonant dipole-dipole) interactions. We explored
transition between the frozen and hot systems, and found that qualitative changes
in dynamics can occur even at :math:`\mu\mathrm{K}` temperatures. Finally, we developed
new efficient theoretical framework for highly disordered (hot) systems.
Obtained non-equilibrium phase transition diagrams can be explored in current
experiments, while the new theoretical framework can help us in describing
complex multi-level, multi-component situations, since it offers efficient,
consistent and expendable framework.
**Reference:** `Phys. Rev. A 94, 011401(R) (2016)`_
Rydberg atoms
-------------
Highly excited atoms, in so-called Rydberg states, have strong atom-atom interactions, and long lifetimes. This makes them flexible platform for both quantum engineering on few-excitation level (light storage, single photon non-linearities, quantum logic gates) and exploration of fundamental physics that opens in the many-body regime with many excitations. Given the inherently non-equilibrium and non-linear nature of this system, understanding the phase diagrams, transitions and ordering in them represents one of the major challenges of the modern physics. All of this has a practical spin-offs too, due to the fact that atoms are sensitive probes of EM fields, with constant and indentical properties everywhere in the Universe.
THz imaging
***********
Atomic vapours provide a medium with properties that are fixed in time, and
easily reproduced. This makes them an excellent resource for metrology. In
particular, wide range of the transitions between the highly excited atoms
corresponds to the terahertz range (0.3-3 THz) in electromagnetic spectrum.
Traditionally, sources and detectors in this range have been scarce, since these
frequencies are too high for usual semiconductor technology on one hand, and too
low for optical technology, on the other.
.. image:: _static/THz_imaging.png
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Recently we managed to achieve atomic excitation (and subsequent observable
fluorescence) proportionally to the THz intensity, allowing mapping of THz field
into optical domain. This is achieved by driving off-resonant optical-terahertz
Raman transition to the excited states. Excitable atomic medium is prepared with
laser ladder driving, which selects atomic velocities, and prevents smearing of
fluorescence pattern, allowing sub-wavelength resolution in 2D. Using usual
resonant Autler-Townes splitting measurements, and calculated values of dipole
matrix elements (that in principle can be fixed to the absolute standards),
measurements are calibrated, providing 3D sub-wavelength THz field sampling,
and simultaneous measurement along 1D. Importantly, since lifetimes of the
excited atomic states are of the order of 10 :math:`\mu\mathrm{s}`, the refresh
rate of the excitable medium is quite fast, allowing real-time maging of dynamic
terahertz fields. This is demonstrated imaging fields at 25fps with consumer camera.
**Reference**: `Nature Photonics 11, 40 (2017)`_
ARC - open source library
*************************
Have you ever wished to be able to quickly perform calculations in Rydberg atomic
physics? From quick estimates during meetings, to easy building up of calculations
from primitives and data at hand, suitably wrapped in useful tools? From asymptotic
C6 coefficients, to Stark maps and spaghetti diagrams, in easily form that
facilitates their exploration and use? Something easy to expand for your own
research purposes? We have developed ARC - Alkali Rydberg Calculator, a
hierarchical Python library of calculation methods and data, precisely with this
in mind. Check our code, detailed .html documentation and iPython notebook with
examples on GitHub (and contribute expansions!).
**Reference:** `Computer Physics Communications 220, 319 (2017)`_
ARC 3.0 expands library, adding support for divalent atoms, and a number of
functions generally useful for atomic physics calculations.
**Reference:** `Computer Physics Communications 261, 107814 (2021)`_
**Online Atom calculator:** `atomcalc.org`_
`Documentation and examples`_
Quantum Optics
--------------
Focusing light with a quantum needle
************************************
For light manipulation we usually employ objects that consists of millions of atoms,
so many of them that we don’t think of individual constituents of mirrors and
lenses we use. Recently attention has been drawn to the question how well we can
control the light if we have only a few atoms. It was shown that even a single
sheet of few dozens of atoms can act as a mirror, which gave rise to a number of
proposals for realising mirrors and lenses consisting of atomically thin layers
with several dozens of individual quantum emitters. The reason for exceptional
efficiency of small atomic ensembles in light control is interference in emission
of the individual dipoles. To achieve such a collective enhancement requires
control in positioning of the individual quantum emitters with sub-wavelength
precision. This sets stringent requirements on experiments, but provides new
pathways for light control: if optical dipoles are to be precisely positioned at
even shorter distances of < λ /(2π), where λ is probing light wavelength, then
one could also exploit cooperative effects stemming from strong dipole-dipole
interactions in the ensemble. For example, interactions can give sharp
frequency-dependant reflectivity of atomic mirrors, while in 1D arrays of atomic
dipoles they can be used for sub-radiant transport in atomically thin wires
and enhanced atom-light interaction cross-sections. Theoretical understanding of
dipolar ensembles is usually provided with models based on linear coupled dipoles,
or small scale full quantum models. This restricts theoretical explanations to
weak driving limit of at most single excitation within the system, where classical
linear coupled-dipole model is valid, or to small ensembles of up to about
dozen atoms, where full quantum calculations can be done.
.. image:: _static/quantum_needle.png
:width: 350
:align: right
In this Letter we explore experimentally and theoretically the ultimate limit of
a lens that has a cross section of a single atom under driving of arbitrary
strength. Depending on detuning from the atomic resonance [Fig 1.(a)], a single atom locally
increases or reduces susceptibility of the medium, acting locally as a convex or
concave lens [Fig. 1(b-c)] respectively. While effect of a single atom is
small, if one positions several atoms in a chain with sub-wavelength precision,
the effect can be collectively enhanced. For light propagating along, such
an atomic chain or “quantum needle” will act for negative (positive) detunings
as focusing (defocusing) lens, giving rise to increasing (decreasing) probability
of excitation of atoms along the chain [Fig. 1(d)]. This collective
response of ensemble of individual quantum dipoles is therefore expected to
give red detuned shift in the resonance fluorescence of the ensemble.
**Reference:** `Phys. Rev. Lett. 124, 253602 (2020)`_
Storing light in motion-insensitive atomic states, and spectroscopy of micrometre-sized blobs
*********************************************************************************************
Storing of light field excitation as a collective excitation of atomic clouds
is important for quantum memories and gates. The storage time so far is limited
by atomic motion that smears out information about the relative phases of the
stored excitation within the cloud, preventing succesful retrival of light in
well defined spatial output channel. This is especially problem for ledder type
excitation to Rydberg states, due to big mismatch of the wavelenghs of light
used for excitation.
.. image:: _static/blob_spectroscopy.png
:width: 250
:align: right
In recent work, we proposed new approach for saving information in the form of
uniform phase spin-waves, that would be insensitive to motion. We showed that by
performing the strong resonant driving of the two excited states, one can get
engineered dressed state, that can be used as a proxy in stadard three-level
storage and retrival protocols. Adiabatic mapping of excitations, used in EIT
based three level storage protocols, can be directly applied in unchanged form
in the new scheme. However, generalised scheme uses actually three lasers and
four states, allowing one to achieve Doppler free excitation of the uniform phase
spin-waves, thus overcoming limitations of storage time due to atomic motion.
Additionaly, off-resonant excitation with three lasers, aranged in plane, allows
one to selectivily (de)excite atoms in very small volume (diameter >10 :math:`\mu\mathrm{m}` )
within bigger cold atomic clouds or vapour cells, which can allow new types of
experiments.
Detailed theoretical discussion of possiblities and limitations is followed with
proof-of-principle experiment.
**Reference:** `Phys. Rev. A 94, 033840 (2016)`_
Collective quantum beats: Should I stay or should I go?
*******************************************************
We have embraced motion of the collective atomic excitation, to store single
photon in superposition of two states: one nearly stationary, while the other
moves away. Observed (collective) quantum beats due to emission of single photon
from both of this states demonstrated coherent nature of the storage.
A single excitation in a quantum world doesn't have to make a decision whether to stay or go.
An excitation can be simultaneously stored in two groups of atoms in a thermal
atomic vapour, allowing a single photon to both ‘stay’ in stationary atoms,
and to ‘go’ with a moving group of atoms.
.. image :: _static/collective_beats.png
:width: 250
:align: right
Atomic vapours usually have a complex, multi-level atomic structure.
Instead of trying to prepare a well-defined initial state of such a system, the
researchers realized a new coherent control scheme by isolating atoms in selected
states. A strong magnetic field and strong laser dressing enables only two atomic
velocity groups to be excited, with well-defined relative phase. Spontaneous
emission then heralds the storage of a single collective excitation of the two
velocity groups; in the lab frame, one group is stationary while the other is moving.
The coherent nature of the storage is demonstrated by observing Doppler-beating
of the single photon simultaneously emitted from the two atomic-velocity groups.
The collective nature of the excitation allows readout of the photons in a
well-defined direction. The demonstrated interferometric measurement scheme
offers possibilities for coherent state manipulation at the single-photon level
in atomic vapour cells, and a way of generating tuneable bi-chromatic photons.
**Reference:** `Phys. Rev. Lett. 118, 253601 (2017)`_
Hyperfine state quantum beats: a new kind of excited state spectroscopy
***********************************************************************
Very short laser pulses, or spontaneous decays, can prepare system in superposition of states with well defined relative phase. If this states happen to decay radiatively, we can see signature of this coherent superposition as oscilation of the fluorescence intensity. This so-called quantum beats happen due to interference of multiple decay paths whose relative phases evolve in time due to differences in energies, imposed external drivings and relative atomic motion (if they are are collective, not single-atom based). We have explored this effect to follow dynamics between two excited states driven by coherent laser field, and observed collapses and rivivals of beating.
**Reference:** `Phys. Rev A 90, 033424 (2014)`_
EIA and EIT in multi-photon excitation schemes
**********************************************
Different excitation schemes can offer not only technological simplifications,
but also new possibilities. We have recently explored four photon Rydberg
excitation scheme, and observed absorptions and transparencies due to complex
multi-level interference effects (EIT and EIA). This was possible even with
a very low laser powers (:math:`\mu\mathrm{W}` and nW)
**Reference:** `Optics Letters 40, 5570 (2015)`_
Atom-surface interactions
-------------------------
**Reference:** `Phys. Rev. A 100, 022503 (2019)`_
`Code and data, with Jupyter notebook showing use.`_
Laser stabilisation
-------------------
**Reference:** `OSA Continuum 1, 4 (2018)`_
`Access to experimental apparatus 3D model fiels for machining.`_
My PhD thesis
-------------
Here are the links for chapters of my thesis "Rydberg atom ensembles under dephasing and dissipation: from single- to many-body dynamics" (Durham University, 2017)
`Introduction`_, Overview of dephasing and dissipation mechanishms and their impact on dynamics. Short history of Rydberg physics.
`Rydberg atomic states: energy level structure and dynamics`_. Check here for more details about ARC project, atomic structure, Rydberg interactions and THz imaging.
`Spin-wave motion`_. Check here for schemes that provide light storage that is insensitive to motion (uniform-phase spin-waves) in ladder storage schemes, and for quantum beat fenomena, both signle-atom qunatum beats, and collective quantum beats.
`Driven-dissipative systems with power-law interactions`_. Check here for more details about non-equilibrium transitions of driven-dissipative systems, occurance of bistability, and impact of spin/atom motion on the non-equilibrium phase diagrams.
`Outlook and conclusion`_.
`Appendix A3 contains derivation of Ensemble Averaged Mean Field`_, that gives analytical solution (equations A.15 and 4.10) for driven-dissipative dynamics of interacting spins that becomes exact solution in the llimit of strong mixing of spins due to fast motion.
.. _`Introduction`: http://etheses.dur.ac.uk/12224/1/Nikola_Sibalic_PhD_thesis_2017.pdf?DDD25+#page=21
.. _`Rydberg atomic states: energy level structure and dynamics` : http://etheses.dur.ac.uk/12224/1/Nikola_Sibalic_PhD_thesis_2017.pdf?DDD25+#page=31
.. _`Spin-wave motion` : http://etheses.dur.ac.uk/12224/1/Nikola_Sibalic_PhD_thesis_2017.pdf?DDD25+#page=63
.. _Driven-dissipative systems with power-law interactions : http://etheses.dur.ac.uk/12224/1/Nikola_Sibalic_PhD_thesis_2017.pdf?DDD25+#page=93
.. _Outlook and conclusion : http://etheses.dur.ac.uk/12224/1/Nikola_Sibalic_PhD_thesis_2017.pdf?DDD25+#page=117
.. _`Appendix A3 contains derivation of Ensemble Averaged Mean Field` : http://etheses.dur.ac.uk/12224/1/Nikola_Sibalic_PhD_thesis_2017.pdf?DDD25+#page=125
.. _Nature Photonics 11, 40 (2017) : http://www.nature.com/nphoton/journal/vaop/ncurrent/full/nphoton.2016.214.html
.. _Phys. Rev. Lett. 124, 253602 (2020) : https://doi.org/10.1103/PhysRevLett.124.253602
.. _Optics Letters 40, 5570 (2015) : http://dx.doi.org/10.1364/OL.40.005570
.. _Phys. Rev A 90, 033424 (2014) : http://journals.aps.org/pra/abstract/10.1103/PhysRevA.90.033424
.. _Phys. Rev. Lett. 118, 253601 (2017) : https://doi.org/10.1103/PhysRevLett.118.253601
.. _Phys. Rev. A 94, 011401(R) (2016) : https://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.011401
.. _Phys. Rev. A 94, 033840 (2016) : http://dx.doi.org/10.1103/PhysRevA.94.033840
.. _Optics Letters 40, 5570 (2015) : http://dx.doi.org/10.1364/OL.40.005570
.. _Computer Physics Communications 220, 319 (2017) : https://doi.org/10.1016/j.cpc.2017.06.015
.. _atomcalc.org : https://atomcalc.org/
.. _Computer Physics Communications 261, 107814 (2021) : https://doi.org/10.1016/j.cpc.2020.107814
.. _Link to PhD thesis. : https//etheses.dur.ac.uk/12224/1/Nikola_Sibalic_PhD_thesis_2017.pdf?DDD25+
.. _Documentation and examples : https://arc-alkali-rydberg-calculator.readthedocs.io/en/latest/index.html
.. _Code and data, with Jupyter notebook showing use. : https://github.com/thermal-vapours/TAS-Transmission-Atom-Surface
.. _OSA Continuum 1, 4 (2018) : https://doi.org/10.1364/OSAC.1.000004
.. _Access to experimental apparatus 3D model fiels for machining. : https://github.com/nikolasibalic/ZSAR-Zeeman-Shifted-Atomic-Reference
.. _`Phys. Rev. A 100, 022503 (2019)` : https://doi.org/10.1103/PhysRevA.100.022503