@article{divincenzo_2000,
    author = {DiVincenzo, David P.},
    title = {The Physical Implementation of Quantum Computation},
    journal = {Fortschritte der Physik},
    volume = {48},
    number = {9-11},
    pages = {771-783},
    doi = {https://doi.org/10.1002/1521-3978(200009)48:9/11%3C771::AID-PROP771%3E3.0.CO;2-E},
    url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/1521-3978%28200009%2948%3A9/11%3C771%3A%3AAID-PROP771%3E3.0.CO%3B2-E},
    eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/1521-3978%28200009%2948%3A9/11%3C771%3A%3AAID-PROP771%3E3.0.CO%3B2-E},
    abstract = {Abstract After a brief introduction to the principles and promise of quantum information processing, the requirements for the physical implementation of quantum computation are discussed. These five requirements, plus two relating to the communication of quantum information, are extensively explored and related to the many schemes in atomic physics, quantum optics, nuclear and electron magnetic resonance spectroscopy, superconducting electronics, and quantum-dot physics, for achieving quantum computing.},
    year = {2000}
}

@Article{macdonell_2021,
    author ="MacDonell, Ryan J. and Dickerson, Claire E. and Birch, Clare J. T. and Kumar, Alok and Edmunds, Claire L. and Biercuk, Michael J. and Hempel, Cornelius and Kassal, Ivan",
    title  ="Analog quantum simulation of chemical dynamics",
    journal  ="Chem. Sci.",
    year  ="2021",
    volume  ="12",
    issue  ="28",
    pages  ="9794-9805",
    publisher  ="The Royal Society of Chemistry",
    doi  ="10.1039/D1SC02142G",
    url  ="http://dx.doi.org/10.1039/D1SC02142G",
    abstract  ="Ultrafast chemical reactions are difficult to simulate because they involve entangled{,} many-body wavefunctions whose computational complexity grows rapidly with molecular size. In photochemistry{,} the breakdown of the Born–Oppenheimer approximation further complicates the problem by entangling nuclear and electronic degrees of freedom. Here{,} we show that analog quantum simulators can efficiently simulate molecular dynamics using commonly available bosonic modes to represent molecular vibrations. Our approach can be implemented in any device with a qudit controllably coupled to bosonic oscillators and with quantum hardware resources that scale linearly with molecular size{,} and offers significant resource savings compared to digital quantum simulation algorithms. Advantages of our approach include a time resolution orders of magnitude better than ultrafast spectroscopy{,} the ability to simulate large molecules with limited hardware using a Suzuki–Trotter expansion{,} and the ability to implement realistic system-bath interactions with only one additional interaction per mode. Our approach can be implemented with current technology; e.g.{,} the conical intersection in pyrazine can be simulated using a single trapped ion. Therefore{,} we expect our method will enable classically intractable chemical dynamics simulations in the near term."
}

@article{yin_2016,
	title = {Measurement-{Device}-{Independent} {Quantum} {Key} {Distribution} {Over} a 404 km {Optical} {Fiber}},
	volume = {117},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.117.190501},
	doi = {10.1103/PhysRevLett.117.190501},
	language = {en},
	number = {19},
	urldate = {2023-07-25},
	journal = {Physical Review Letters},
	author = {Yin, Hua-Lei and Chen, Teng-Yun and Yu, Zong-Wen and Liu, Hui and You, Li-Xing and Zhou, Yi-Heng and Chen, Si-Jing and Mao, Yingqiu and Huang, Ming-Qi and Zhang, Wei-Jun and Chen, Hao and Li, Ming Jun and Nolan, Daniel and Zhou, Fei and Jiang, Xiao and Wang, Zhen and Zhang, Qiang and Wang, Xiang-Bin and Pan, Jian-Wei},
	month = nov,
	year = {2016},
	pages = {190501},
}

@article{kimble_2008,
	title = {The quantum internet},
	volume = {453},
	issn = {0028-0836, 1476-4687},
	url = {https://www.nature.com/articles/nature07127},
	doi = {10.1038/nature07127},
	language = {en},
	number = {7198},
	urldate = {2023-12-11},
	journal = {Nature},
	author = {Kimble, H. J.},
	month = jun,
	year = {2008},
	pages = {1023--1030},
}

@article{rosenfeld_2017,
	title = {Event-{Ready} {Bell} {Test} {Using} {Entangled} {Atoms} {Simultaneously} {Closing} {Detection} and {Locality} {Loopholes}},
	volume = {119},
	issn = {0031-9007, 1079-7114},
	url = {http://link.aps.org/doi/10.1103/PhysRevLett.119.010402},
	doi = {10.1103/PhysRevLett.119.010402},
	language = {en},
	number = {1},
	urldate = {2023-12-11},
	journal = {Physical Review Letters},
	author = {Rosenfeld, Wenjamin and Burchardt, Daniel and Garthoff, Robert and Redeker, Kai and Ortegel, Norbert and Rau, Markus and Weinfurter, Harald},
	month = jul,
	year = {2017},
	pages = {010402},
}

@article{giovannetti_2004,
	title = {Quantum-{Enhanced} {Measurements}: {Beating} the {Standard} {Quantum} {Limit}},
	volume = {306},
	issn = {0036-8075, 1095-9203},
	shorttitle = {Quantum-{Enhanced} {Measurements}},
	url = {https://www.science.org/doi/10.1126/science.1104149},
	doi = {10.1126/science.1104149},
	language = {en},
	number = {5700},
	urldate = {2023-12-11},
	journal = {Science},
	author = {Giovannetti, Vittorio and Lloyd, Seth and Maccone, Lorenzo},
	month = nov,
	year = {2004},
	pages = {1330--1336},
}

@article{bennett_brassard_2014,
	title = {Quantum cryptography: {Public} key distribution and coin tossing},
	volume = {560},
	issn = {03043975},
	shorttitle = {Quantum cryptography},
	url = {https://linkinghub.elsevier.com/retrieve/pii/S0304397514004241},
	doi = {10.1016/j.tcs.2014.05.025},
	language = {en},
	urldate = {2023-12-11},
	journal = {Theoretical Computer Science},
	author = {Bennett, Charles H. and Brassard, Gilles},
	month = dec,
	year = {2014},
	pages = {7--11},
}

@article{briegel_1998,
  title = {Quantum Repeaters: The Role of Imperfect Local Operations in Quantum Communication},
  author = {Briegel, H.-J. and D\"ur, W. and Cirac, J. I. and Zoller, P.},
  journal = {Phys. Rev. Lett.},
  volume = {81},
  issue = {26},
  pages = {5932--5935},
  numpages = {0},
  year = {1998},
  month = {Dec},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.81.5932},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.81.5932}
}

@article{lambert_2020,
    author = {Lambert, Nicholas J. and Rueda, Alfredo and Sedlmeir, Florian and Schwefel, Harald G. L.},
    title = {Coherent Conversion Between Microwave and Optical Photons—An Overview of Physical Implementations},
    journal = {Advanced Quantum Technologies},
    volume = {3},
    number = {1},
    pages = {1900077},
    keywords = {microwave to optical transduction, nonlinear optics, quantum communication, quantum optics},
    doi = {https://doi.org/10.1002/qute.201900077},
    url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/qute.201900077},
    eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/qute.201900077},
    abstract = {Abstract Quantum information technology based on solid state qubits has created much interest in converting quantum states from the microwave to the optical domain. Optical photons, unlike microwave photons, can be transmitted by fiber, making them suitable for long distance quantum communication. Moreover, the optical domain offers access to a large set of very well-developed quantum optical tools, such as highly efficient single-photon detectors and long-lived quantum memories. For a high fidelity microwave to optical transducer, efficient conversion at single photon level and low added noise is needed. Currently, the most promising approaches to build such systems are based on second-order nonlinear phenomena such as optomechanical and electro-optic interactions. Alternative approaches, although not yet as efficient, include magneto-optical coupling and schemes based on isolated quantum systems like atoms, ions, or quantum dots. Herein, the necessary theoretical foundations for the most important microwave-to-optical conversion experiments are provided, their implementations are described, and the current limitations and future prospects are discussed.},
    year = {2020}
}

@article{lauk_2020,
    doi = {10.1088/2058-9565/ab788a},
    url = {https://dx.doi.org/10.1088/2058-9565/ab788a},
    year = {2020},
    month = {mar},
    publisher = {IOP Publishing},
    volume = {5},
    number = {2},
    pages = {020501},
    author = {Nikolai Lauk and Neil Sinclair and Shabir Barzanjeh and Jacob P Covey and Mark Saffman and Maria Spiropulu and Christoph Simon},
    title = {Perspectives on quantum transduction},
    journal = {Quantum Science and Technology},
    abstract = {Quantum transduction, the process of converting quantum signals from one form of energy to another, is an important area of quantum science and technology. The present perspective article reviews quantum transduction between microwave and optical photons, an area that has recently seen a lot of activity and progress because of its relevance for connecting superconducting quantum processors over long distances, among other applications. Our review covers the leading approaches to achieving such transduction, with an emphasis on those based on atomic ensembles, opto-electro-mechanics, and electro-optics. We briefly discuss relevant metrics from the point of view of different applications, as well as challenges for the future.}
}

@article{rueda_2016,
    author = {Alfredo Rueda and Florian Sedlmeir and Michele C. Collodo and Ulrich Vogl and Birgit Stiller and Gerhard Schunk and Dmitry V. Strekalov and Christoph Marquardt and Johannes M. Fink and Oskar Painter and Gerd Leuchs and Harald G. L. Schwefel},
    journal = {Optica},
    keywords = {Upconversion; Electro-optical devices; Nonlinear wave mixing ; Optical circuits; Optical networks; Phase modulation; Q factor; Quantum memories; Sum frequency generation},
    number = {6},
    pages = {597--604},
    publisher = {Optica Publishing Group},
    title = {Efficient microwave to optical photon conversion: an electro-optical realization},
    volume = {3},
    month = {Jun},
    year = {2016},
    url = {https://opg.optica.org/optica/abstract.cfm?URI=optica-3-6-597},
    doi = {10.1364/OPTICA.3.000597},
    abstract = {Linking classical microwave electrical circuits to the optical telecommunication band is at the core of modern communication. Future quantum information networks will require coherent microwave-to-optical conversion to link electronic quantum processors and memories via low-loss optical telecommunication networks. Efficient conversion can be achieved with electro-optical modulators operating at the single microwave photon level. In the standard electro-optic modulation scheme, this is impossible because both up- and down-converted sidebands are necessarily present. Here, we demonstrate true single-sideband up- or down-conversion in a triply resonant whispering gallery mode resonator by explicitly addressing modes with asymmetric free spectral range. Compared to previous experiments, we show a 3 orders of magnitude improvement of the electro-optical conversion efficiency, reaching 0.1\% photon number conversion for a 10 GHz microwave tone at 0.42 mW of optical pump power. The presented scheme is fully compatible with existing superconducting 3D circuit quantum electrodynamics technology and can be used for nonclassical state conversion and communication. Our conversion bandwidth is larger than 1 MHz and is not fundamentally limited.},
}

@article{rueda_2019,
    title={Electro-optic entanglement source for microwave to telecom quantum state transfer},
    author={Rueda, Alfredo and Hease, William and Barzanjeh, Shabir and Fink, Johannes M},
    journal={npj Quantum Information},
    volume={5},
    number={1},
    pages={108},
    year={2019},
    publisher={Nature Publishing Group UK London}
}

@article{sahu_2023,
    author = {R. Sahu  and L. Qiu  and W. Hease  and G. Arnold  and Y. Minoguchi  and P. Rabl  and J. M. Fink },
    title = {Entangling microwaves with light},
    journal = {Science},
    volume = {380},
    number = {6646},
    pages = {718-721},
    year = {2023},
    doi = {10.1126/science.adg3812},
    URL = {https://www.science.org/doi/abs/10.1126/science.adg3812},
    eprint = {https://www.science.org/doi/pdf/10.1126/science.adg3812},
    abstract = {Quantum entanglement is a key resource in currently developed quantum technologies. Sharing this fragile property between superconducting microwave circuits and optical or atomic systems would enable new functionalities, but this has been hindered by an energy scale mismatch of \&gt;104 and the resulting mutually imposed loss and noise. In this work, we created and verified entanglement between microwave and optical fields in a millikelvin environment. Using an optically pulsed superconducting electro-optical device, we show entanglement between propagating microwave and optical fields in the continuous variable domain. This achievement not only paves the way for entanglement between superconducting circuits and telecom wavelength light, but also has wide-ranging implications for hybrid quantum networks in the context of modularization, scaling, sensing, and cross-platform verification. Several platforms are under development for quantum computation, simulation, and metrology applications, with each platform operating at different operational wavelengths for optimized performance. For practical technologies, the reality will likely be a hybrid of platforms that require quantum entanglement to be generated and shared across platforms with a large energy disparity. Sahu et al. introduce an electro-optical device that allows the generation of quantum entanglement between microwaves (the operational wavelengths of superconducting circuits) with optical photons (the operational wavelength of long-distance quantum communication). Bridging platforms with more than five orders of magnitude difference in energy scales and maintaining the fragile entanglement provides a route to efficiently linking up hybrid quantum systems. —Ian S. Osborne An electro-optical device is developed to generate quantum entanglement between microwave and optical photon pairs.}
}

@article{bochmann_2013,
    title={Nanomechanical coupling between microwave and optical photons},
    author={Bochmann, Joerg and Vainsencher, Amit and Awschalom, David D and Cleland, Andrew N},
    journal={Nature Physics},
    volume={9},
    number={11},
    pages={712--716},
    year={2013},
    publisher={Nature Publishing Group UK London}
}

@article{higginbotham_2018,
    title={Harnessing electro-optic correlations in an efficient mechanical converter},
    author={Higginbotham, Andrew P and Burns, PS and Urmey, MD and Peterson, RW and Kampel, NS and Brubaker, BM and Smith, G and Lehnert, KW and Regal, CA},
    journal={Nature Physics},
    volume={14},
    number={10},
    pages={1038--1042},
    year={2018},
    publisher={Nature Publishing Group UK London}
}

@article{hisatomi_2016,
    title = {Bidirectional conversion between microwave and light via ferromagnetic magnons},
    author = {Hisatomi, R. and Osada, A. and Tabuchi, Y. and Ishikawa, T. and Noguchi, A. and Yamazaki, R. and Usami, K. and Nakamura, Y.},
    journal = {Phys. Rev. B},
    volume = {93},
    issue = {17},
    pages = {174427},
    numpages = {13},
    year = {2016},
    month = {May},
    publisher = {American Physical Society},
    doi = {10.1103/PhysRevB.93.174427},
    url = {https://link.aps.org/doi/10.1103/PhysRevB.93.174427}
}

@article{staudt_2012,
    doi = {10.1088/0953-4075/45/12/124019},
    url = {https://dx.doi.org/10.1088/0953-4075/45/12/124019},
    year = {2012},
    month = {jun},
    publisher = {IOP Publishing},
    volume = {45},
    number = {12},
    pages = {124019},
    author = {Matthias U Staudt and Io-Chun Hoi and Philip Krantz and Martin Sandberg and Michaël Simoen and Pavel Bushev and Nicolas Sangouard and Mikael Afzelius and Vitaly S Shumeiko and Göran Johansson and Per Delsing and C M Wilson},
    title = {Coupling of an erbium spin ensemble to a superconducting resonator},
    journal = {Journal of Physics B: Atomic, Molecular and Optical Physics},
    abstract = {A quantum coherent interface between optical and microwave photons can be used as a basic building block within a future quantum information network. The interface is envisioned as an ensemble of rare-earth ions coupled to a superconducting resonator, allowing for coherent transfer between optical and microwave photons. Towards this end, we have realized a hybrid device coupling a Er3 +-doped Y2SiO5 crystal in a superconducting coplanar waveguide cavity. We observe a collective spin coupling of 4 MHz and a spin linewidth of down to 75 MHz.}
}

@book{faul_book,
	address = {Boca Raton},
	title = {A concise introduction to numerical analysis},
	isbn = {978-1-4987-1218-7},
	language = {en},
	publisher = {CRC Press, Taylor \& Francis Group},
	author = {Faul, A. C.},
	year = {2016},
	keywords = {Numerical analysis, Textbooks},
}

@article{probst_2013,
    title = {Anisotropic Rare-Earth Spin Ensemble Strongly Coupled to a Superconducting Resonator},
    author = {Probst, S. and Rotzinger, H. and W\"unsch, S. and Jung, P. and Jerger, M. and Siegel, M. and Ustinov, A. V. and Bushev, P. A.},
    journal = {Phys. Rev. Lett.},
    volume = {110},
    issue = {15},
    pages = {157001},
    numpages = {5},
    year = {2013},
    month = {Apr},
    publisher = {American Physical Society},
    doi = {10.1103/PhysRevLett.110.157001},
    url = {https://link.aps.org/doi/10.1103/PhysRevLett.110.157001}
}

@article{ranvcic_2018,
    title={Coherence time of over a second in a telecom-compatible quantum memory storage material},
    author={Ran{\v{c}}i{\'c}, Milo{\v{s}} and Hedges, Morgan P and Ahlefeldt, Rose L and Sellars, Matthew J},
    journal={Nature Physics},
    volume={14},
    number={1},
    pages={50--54},
    year={2018},
    publisher={Nature Publishing Group UK London}
}

@article{zhong_2015,
    title={Optically addressable nuclear spins in a solid with a six-hour coherence time},
    author={Zhong, Manjin and Hedges, Morgan P and Ahlefeldt, Rose L and Bartholomew, John G and Beavan, Sarah E and Wittig, Sven M and Longdell, Jevon J and Sellars, Matthew J},
    journal={Nature},
    volume={517},
    number={7533},
    pages={177--180},
    year={2015},
    publisher={Nature Publishing Group UK London}
}

@article{le_dantec_2021,
    author = {Marianne Le Dantec  and Miloš Rančić  and Sen Lin  and Eric Billaud  and Vishal Ranjan  and Daniel Flanigan  and Sylvain Bertaina  and Thierry Chanelière  and Philippe Goldner  and Andreas Erb  and Ren Bao Liu  and Daniel Estève  and Denis Vion  and Emmanuel Flurin  and Patrice Bertet },
    title = {Twenty-three–millisecond electron spin coherence of erbium ions in a natural-abundance crystal},
    journal = {Science Advances},
    volume = {7},
    number = {51},
    pages = {eabj9786},
    year = {2021},
    doi = {10.1126/sciadv.abj9786},
    URL = {https://www.science.org/doi/abs/10.1126/sciadv.abj9786},
    eprint = {https://www.science.org/doi/pdf/10.1126/sciadv.abj9786},
    abstract = {A scheelite crystal with residual concentration of erbium is cooled down to 10 mK, yielding a record spin coherence time of 23 ms. Erbium ions embedded in crystals have unique properties for quantum information processing, because of their optical transition at 1.5 μm and of the large magnetic moment of their effective spin-1/2 electronic ground state. Most applications of erbium require, however, long electron spin coherence times, and this has so far been missing. Here, by selecting a host matrix with a low nuclear-spin density (CaWO4) and by quenching the spectral diffusion due to residual paramagnetic impurities at millikelvin temperatures, we obtain a 23-ms coherence time on the Er3+ electron spin transition. This is the longest Hahn echo electron spin coherence time measured in a material with a natural abundance of nuclear spins and on a magnetically sensitive transition. Our results establish Er3+:CaWO4 as a potential platform for quantum networks.}
}

@article{bottger_2009,
  title = {Effects of magnetic field orientation on optical decoherence in ${\text{Er}}^{3+}:{\text{Y}}_{2}{\text{SiO}}_{5}$},
  author = {B\"ottger, Thomas and Thiel, C. W. and Cone, R. L. and Sun, Y.},
  journal = {Phys. Rev. B},
  volume = {79},
  issue = {11},
  pages = {115104},
  numpages = {8},
  year = {2009},
  month = {Mar},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.79.115104},
  url = {https://link.aps.org/doi/10.1103/PhysRevB.79.115104}
}

@article{vleck_1937,
    author = {Vleck, J. H. Van.},
    title = {The Puzzle of Rare-earth Spectra in Solids.},
    journal = {The Journal of Physical Chemistry},
    volume = {41},
    number = {1},
    pages = {67-80},
    year = {1937},
    doi = {10.1021/j150379a006},
    URL = {https://doi.org/10.1021/j150379a006},
    eprint = {https://doi.org/10.1021/j150379a006}
}

@book{wybourne_book,
    title={Spectroscopic Properties of Rare Earths},
    author={Wybourne, B.G.},
    isbn={9780470965078},
    lccn={lc65012697},
    url={https://books.google.com.au/books?id=I91EAAAAIAAJ},
    year={1965},
    publisher={Interscience Publishers}
}

@book{gerry_knight_book,
    title={Introductory Quantum Optics},
    publisher={Cambridge University Press},
    author={Gerry, Christopher and Knight, Peter},
    year={2005},
    ISBN={9780521527354}
}

@ARTICLE{jaynes_cummings_1963,
    author={Jaynes, E.T. and Cummings, F.W.},
    journal={Proceedings of the IEEE}, 
    title={Comparison of quantum and semiclassical radiation theories with application to the beam maser}, 
    year={1963},
    volume={51},
    number={1},
    pages={89-109},
    doi={10.1109/PROC.1963.1664}
}

@book{sakurai_book,
    author = {Sakurai, J. J. (Jun John) and Napolitano, Jim},
    address = {Cambridge},
    booktitle = {Modern Quantum Mechanics},
    edition = {Third edition.},
    isbn = {9781108587280},
    keywords = {Quantum theory$$QQuantum theory -- Textbooks},
    language = {eng},
    publisher = {Cambridge University Press},
    title = {Modern Quantum Mechanics},
    year = {2021}
}

@book{breuer_book,
    author = {Breuer, Heinz-Peter and Petruccione, Francesco},
    title = "{The Theory of Open Quantum Systems}",
    publisher = {Oxford University Press},
    year = {2007},
    month = {01},
    isbn = {9780199213900},
    doi = {10.1093/acprof:oso/9780199213900.001.0001},
    url = {https://doi.org/10.1093/acprof:oso/9780199213900.001.0001},
}

@article{gardiner_collett_1985,
    title = {Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation},
    author = {Gardiner, C. W. and Collett, M. J.},
    journal = {Phys. Rev. A},
    volume = {31},
    issue = {6},
    pages = {3761--3774},
    year = {1985},
    month = {Jun},
    publisher = {American Physical Society},
    doi = {10.1103/PhysRevA.31.3761},
    url = {https://link.aps.org/doi/10.1103/PhysRevA.31.3761}
}

@book{walls_milburn_book,
    author = {Walls, D.F and Milburn, Gerard J},
    address = {Berlin, Heidelberg},
    edition = {2nd ed.},
    isbn = {3540285741},
    keywords = {Classical Electrodynamics ;  Elementary Particles, Quantum Field Theory ;  Optics, Lasers, Photonics, Optical Devices ;  Physics ;  Physics and Astronomy ;  Physics. Light and infrared and ultraviolet phenomena ;  Quantum Information Technology, Spintronics ;  Quantum Optics ;  Quantum Physics},
    language = {eng},
    publisher = {Springer Nature},
    title = {Quantum Optics},
    year = {2008}
}

@article{williamson_2014,
    title = {Magneto-Optic Modulator with Unit Quantum Efficiency},
    author = {Williamson, Lewis A. and Chen, Yu-Hui and Longdell, Jevon J.},
    journal = {Phys. Rev. Lett.},
    volume = {113},
    issue = {20},
    pages = {203601},
    numpages = {5},
    year = {2014},
    month = {Nov},
    publisher = {American Physical Society},
    doi = {10.1103/PhysRevLett.113.203601},
    url = {https://link.aps.org/doi/10.1103/PhysRevLett.113.203601}
}

@article{brion_2007,
    doi = {10.1088/1751-8113/40/5/011},
    url = {https://dx.doi.org/10.1088/1751-8113/40/5/011},
    year = {2007},
    month = {jan},
    publisher = {},
    volume = {40},
    number = {5},
    pages = {1033},
    author = {E Brion and L H Pedersen and K Mølmer},
    title = {Adiabatic elimination in a lambda system},
    journal = {Journal of Physics A: Mathematical and Theoretical},
    abstract = {This paper deals with different ways to extract the effective two-dimensional lower level dynamics of a lambda system excited by off-resonant laser beams. We present a commonly used procedure for elimination of the upper level, and we show that it may lead to ambiguous results. To overcome this problem and better understand the applicability conditions of this scheme, we review two rigorous methods which allow us both to derive an unambiguous effective two-level Hamiltonian of the system and to quantify the accuracy of the approximation achieved: the first relies on the exact solution of the Schrödinger equation, while the second resorts to the Green's function formalism and the Feshbach projection operator technique.}
}

@article{fernandez-gonzalvo_2019,
    title = {Cavity-enhanced Raman heterodyne spectroscopy in ${\mathrm{Er}}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ for microwave to optical signal conversion},
    author = {Fernandez-Gonzalvo, Xavier and Horvath, Sebastian P. and Chen, Yu-Hui and Longdell, Jevon J.},
    journal = {Phys. Rev. A},
    volume = {100},
    issue = {3},
    pages = {033807},
    numpages = {9},
    year = {2019},
    month = {Sep},
    publisher = {American Physical Society},
    doi = {10.1103/PhysRevA.100.033807},
    url = {https://link.aps.org/doi/10.1103/PhysRevA.100.033807}
}

@article{barnett_longdell_2020,
    title = {Theory of microwave-optical conversion using rare-earth-ion dopants},
    author = {Barnett, Peter S. and Longdell, Jevon J.},
    journal = {Phys. Rev. A},
    volume = {102},
    issue = {6},
    pages = {063718},
    numpages = {9},
    year = {2020},
    month = {Dec},
    publisher = {American Physical Society},
    doi = {10.1103/PhysRevA.102.063718},
    url = {https://link.aps.org/doi/10.1103/PhysRevA.102.063718}
}

@mastersthesis{barnett_msc,
    title = {Theory of Microwave to Optical Photon Upconversion Using Erbium Doped Crystals},
    author = {Barnett, Peter S.},
    school = {University of Otago},
    year = {2019}
}

@article{bartholomew_chip_2020,
	title = {On-chip coherent microwave-to-optical transduction mediated by ytterbium in {YVO4}},
	volume = {11},
	issn = {2041-1723},
	url = {https://www.nature.com/articles/s41467-020-16996-x},
	doi = {10.1038/s41467-020-16996-x},
	abstract = {Abstract
            Optical networks that distribute entanglement among various quantum systems will form a powerful framework for quantum science but are yet to interface with leading quantum hardware such as superconducting qubits. Consequently, these systems remain isolated because microwave links at room temperature are noisy and lossy. Building long distance connectivity requires interfaces that map quantum information between microwave and optical fields. While preliminary microwave-to-optical transducers have been realized, developing efficient, low-noise devices that match superconducting qubit frequencies (gigahertz) and bandwidths (10 kilohertz – 1 megahertz) remains a challenge. Here we demonstrate a proof-of-concept on-chip transducer using trivalent ytterbium-171 ions in yttrium orthovanadate coupled to a nanophotonic waveguide and a microwave transmission line. The device′s miniaturization, material, and zero-magnetic-field operation are important advances for rare-earth ion magneto-optical devices. Further integration with high quality factor microwave and optical resonators will enable efficient transduction and create opportunities toward multi-platform quantum networks.},
	language = {en},
	number = {1},
	urldate = {2023-08-08},
	journal = {Nature Communications},
	author = {Bartholomew, John G. and Rochman, Jake and Xie, Tian and Kindem, Jonathan M. and Ruskuc, Andrei and Craiciu, Ioana and Lei, Mi and Faraon, Andrei},
	month = jun,
	year = {2020},
	pages = {3266}
}

@article{kindem_characterization_2018,
	title = {Characterization of {Yb} 3 + 171 : {YVO} 4 for photonic quantum technologies},
	volume = {98},
	issn = {2469-9950, 2469-9969},
	shorttitle = {Characterization of {Yb} 3 + 171},
	url = {https://link.aps.org/doi/10.1103/PhysRevB.98.024404},
	doi = {10.1103/PhysRevB.98.024404},
	language = {en},
	number = {2},
	urldate = {2023-09-11},
	journal = {Physical Review B},
	author = {Kindem, Jonathan M. and Bartholomew, John G. and Woodburn, Philip J. T. and Zhong, Tian and Craiciu, Ioana and Cone, Rufus L. and Thiel, Charles W. and Faraon, Andrei},
	month = jul,
	year = {2018},
	pages = {024404}
}

@article{kindem_control_2020,
	title = {Control and single-shot readout of an ion embedded in a nanophotonic cavity},
	volume = {580},
	issn = {0028-0836, 1476-4687},
	url = {https://www.nature.com/articles/s41586-020-2160-9},
	doi = {10.1038/s41586-020-2160-9},
	language = {en},
	number = {7802},
	urldate = {2023-09-22},
	journal = {Nature},
	author = {Kindem, Jonathan M. and Ruskuc, Andrei and Bartholomew, John G. and Rochman, Jake and Huan, Yan Qi and Faraon, Andrei},
	month = apr,
	year = {2020},
	pages = {201--204}
}

@article{ranon_1968,
    title = {Paramagnetic resonance of Nd3+, Dy3+, Er3+ and Yb3+ in YVO4},
    journal = {Physics Letters A},
    volume = {28},
    number = {3},
    pages = {228-229},
    year = {1968},
    issn = {0375-9601},
    doi = {https://doi.org/10.1016/0375-9601(68)90218-1},
    url = {https://www.sciencedirect.com/science/article/pii/0375960168902181},
    author = {U. Ranon},
    abstract = {The paramagnetic resonance spectra of Nd3+, Dy3+, Er3+ and Yb3+ in YVO4 were measured at X and Ka bands and at 4.2 and 1.8°K. Spin Hamiltonian parameters were determined and the ground state eigen-functions are discussed. The relaxation time of Er3+ was measured at X band.}
}

@article{chen_2021,
  title = {Optically Unstable Phase from Ion-Ion Interactions in an Erbium-Doped Crystal},
  author = {Chen, Yu-Hui and Horvath, Sebastian P. and Longdell, Jevon J. and Zhang, Xiangdong},
  journal = {Phys. Rev. Lett.},
  volume = {126},
  issue = {11},
  pages = {110601},
  numpages = {6},
  year = {2021},
  month = {Mar},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.126.110601},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.126.110601}
}

@misc{faraon_personal,
    author = "Tian Xie, Riku Fukumori, and Andrei Faraon",
    date = "2024-01-23",
    howpublished = "personal communication"
}

@book{yvo_book,
    title = {Handbook of Laser Science and Technology, Vol. V: Optical materials},
    author = {Weber, Marvin J.},
    publisher = {CRC Press},
    year = {1987},
    isbn = {0-8493-3505-1},
    pages = {283}
}

@article{baur_2009,
  title = {Measurement of Autler-Townes and Mollow Transitions in a Strongly Driven Superconducting Qubit},
  author = {Baur, M. and Filipp, S. and Bianchetti, R. and Fink, J. M. and G\"oppl, M. and Steffen, L. and Leek, P. J. and Blais, A. and Wallraff, A.},
  journal = {Phys. Rev. Lett.},
  volume = {102},
  issue = {24},
  pages = {243602},
  numpages = {4},
  year = {2009},
  month = {Jun},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.102.243602},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.102.243602}
}
