Induced THz transitions in Rydberg caesium atoms for application in antihydrogen experiments
Mélissa Vieille-Grosjean, Emiliya Dimova, Zeudi Mazzotta, Daniel Comparat, Tim Wolz, Chloé Malbrunot
IInduced THz transitions in Rydberg caesium atoms for application in antihydrogenexperiments
M. Vieille-Grosjean, Z. Mazzotta, ∗ and D. Comparat Universit´e Paris-Saclay, CNRS, Laboratoire Aim´e Cotton, 91405, Orsay, France
E. Dimova † Bulgarian Academy of Sciences, 72 Tzarigradsko Chauss´ee Blvd., 1784 Sofia, Bulgaria
T. Wolz and C. Malbrunot
Physics Department, CERN, Gen`eve 23, 1211, Switzerland (Dated: January 27, 2021)Antihydrogen atoms are produced at CERN in highly excited Rydberg states. However, precisionmeasurements require anti-atoms in ground state. Whereas experiments currently rely on sponta-neous emission only, simulations have shown that THz light can be used to stimulate the decaytowards ground state and thus increase the number of anti-atoms available for measurements. Wereview different possibilities at hand to generate light in the THz range required for the purpose ofstimulated deexcitation. We demonstrate the effect of a blackbody type light source, which howeverpresents drawbacks for this application including strong photoionization. Further, we report on thefirst THz transitions in a beam of Rydberg caesium atoms induced by photomixers and concludewith the implications of the results for the antihydrogen case.
I. INTRODUCTION
After years of technical developments, antihydrogen( ¯H) atoms can be regularly produced at CERN’s Antipro-ton Decelerator complex [1–3]. This anti-atom is used forstringent tests of the Charge-Parity-Time (CPT) symme-try as well as for the direct measurements of the effectof the Earth’s gravitational acceleration on antimatter.For precision measurements towards both of these goalsground-state antihydrogen atoms are needed.The atoms are mostly synthesized using either a chargeexchange (CE) reaction where an excited positronium(Ps) atom (bound state of an electron and a positron)releases its positron to an antiproton or a so-called three-body recombination reaction (3BR) where a large num-ber of positrons and antiprotons are brought together toform antihydrogen.Both formation mechanisms produce antihydrogenatoms in highly excited Rydberg states with so-far bestachieved temperatures of ∼
40 K [1] (corresponding toa mean velocity of ∼ / s) and in the presence ofrelatively strong magnetic fields ( O (1 T)) to confine thecharged particles and, in some cases, trap the antihydro-gen atoms. Although experimentally not well studied,the antihydrogen atoms formed via 3BR are expected tocover a broad range of principle quantum numbers up to n ∼
100 [4–8]. Highly excited states will be ionized by theelectric field present at the edges of the charged cloudsso that in general only antihydrogen with n <
50 can es-cape the formation region. Via the CE reaction, specific ∗ Present address:
Advanced Research Center for Nano-lithography (ARCNL), Science Park 106, 1098 XG, The Nether-lands † deceased September 08, 2020 n ∼
30 values can be targeted resulting in a narrowerspread in n that is mainly determined by the velocityand velocity distribution of the impinging Ps [9–11]. Ineither case, all ( k, m ) substates are populated where m is the magnetic quantum number and k a labeling indexaccording to the strength of the substate’s diamagneticinteraction that becomes in a field-free environment theangular momentum quantum number l . The field-freelifetime τ n,l of the Rydberg states produced τ n,l ≈ (cid:16) n (cid:17) (cid:18) l + 1 / (cid:19) × . B ∼ a r X i v : . [ phy s i c s . a t o m - ph ] J a n viding some insights into the antihydrogen deexcitationschemes dealt with and clarifying which light intensitiesand wavelengths are required in section II, we analyse insection III the suitability of different THz light sourcesfor this purpose. We report in section IV on the effect of abroadband lamp and on the first observation of highly se-lective THz light stimulated population transfer betweenRydberg states with a photomixer in a proof-of-principleexperiment with a beam of excited caesium atoms. II. THZ-INDUCED ANTIHYDROGENDEEXCITATION AND STATE MIXING
For both production schemes, CE and 3BR, the ideaof stimulated deexcitation of antihydrogen comes downto mixing many initially populated long-lived states andsimultaneously driving transitions to fewer short lived-levels from where the spontaneous cascade decay towardsthe ground state is fast. Relying on a pulsed CE produc-tion scheme the initially populated states can be mixedby applying an additional electric field to the alreadypresent magnetic one [16]. A deexcitation/mixing schemebased on the stimulation of atomic transitions via light inthe THz frequency range is thoroughly discussed in [14]for the 3BR case. This latter scheme is equally applicableto a pulsed CE production.When coupling a distribution of N long-lived levelswith an average lifetime of τ N to N (cid:48) levels with an aver-age deexcitation time to ground state of τ GSN (cid:48) (cid:28) τ N , theminimum achievable time t deex for the entire system todecay to ground state can be approximated by t deex ≈ NN (cid:48) × τ GS N (cid:48) . (2)In (anti)hydrogen, the average decay time of a n (cid:48) -manifold with N (cid:48) fully mixed states to ground state canbe approximated, for low n (cid:48) , by the average lifetime ofthe manifold: τ GS N (cid:48) ∼ µ s × ( n (cid:48) / . [16]. Consequently,when coupling some thousands of initially populated Ry-dberg antihydrogen levels ( n ∼
30) to a low lying mani-fold this intrinsic limit would lead to a best deexcitationtime towards ground state of roughly a few tens of µ s.Within such a time interval the atoms move only by a fewtens of mm and thus stay close to the formation regionfrom where, once deexcited, a beam can be efficientlyformed.Figure 1 shows the binding energy diagram of anti-hydrogen states in a 1 T magnetic field. Recalling the | ∆ m | = 1 selection rule, it becomes apparent that, es-pecially to address high angular momentum states thatare incidentally the longest lived ones, all ∆ n = − n = − n manifold transitions from Ry-dberg levels ( n, k, m ) down towards a manifold n (cid:48) thatis rapidly depopulated to ground state by spontaneous FIG. 1. Binding energy of (anti-)hydrogen Rydberg states ina 1 T magnetic field as a function of the magnetic quantumnumber m . Inter- n manifold transitions in the THz region areindicated by continuous errors. Dashed arrows illustrate someexamples of spontaneous transitions. The figure is adaptedfrom Ref. [14]. emission (in the following referred to as THz deexcita-tion) is studied.For n = 30 and n (cid:48) = 5 it is found that the total(summed over all driven transitions) light intensity nec-essary is of >
10 mW / cm covering a frequency rangefrom ∼
200 GHz to well within the few THz region (thefrequencies range from over 40 THz for n = 6 → n = 30 → k, m ) sublevels within, for example,25 ≤ n ≤
35. Retaining the levels equipopulated allowsfor a narrowband deexcitation laser to couple the Ryd-berg state distribution directly to the n = 3 manifoldwhich decays on a nanosecond timescale. This results ina reduction of the total THz light intensity required bymore than an order of magnitude to 1 mW / cm .In summary, THz mixing or deexcitation requires thesimultaneous generation of multiple light frequencies inthe mW power regime. As derived in Ref. [14], optimalconditions to transfer population are given when sendingequally intense light to stimulate the desired individual n → n − III. THZ SOURCES
The spectral range in the THz region – also called far-infrared or sub-mm region, depending on the commu-nity (1 THz corresponds to 33 cm − , to ∼ A. Narrowband THz sources
In the case of narrowband sources, particular atomictransitions can be targeted and therefore the power pro-vided by the source at those wavelengths is entirely usedto drive the transition. Thus, ionization due to off-resonant wavelengths can be minimized. The usage ofmultiple sources allows to implement the correct powerscaling as a function of output frequency increasing theefficiency of the deexcitation. However, when stimulat-ing all ∆ n = − n = 30 down to n (cid:48) = 5a totality of 25 wavelengths is required. In the presenceof a magnetic field which leads to significant degener-acy lifting of the levels, the necessary number of (very)narrowband sources can even increase further due to thespectral broadening of the atomic transitions. In viewof the high number of desired wavelengths that need tobe produced the usage of expensive direct synthesis suchas quantum cascade or molecular lasers is not an option.Furthermore, as mentioned earlier, the exact distributionof quantum states populated during antihydrogen syn-thesis is not well known and thus a versatile apparatus isneeded to adapt the frequencies generated and used formixing. Given this point, CMOS-based terahertz sourcesor powerful diodes ( > n different laserfrequencies ν i input signals, the photomixer optical beat-note produces, in the ultra-fast semiconductor material,THz waves at all ν i − ν j frequencies; the number of whichbeing n ( n − /
2. Photomixing can nowadays reachthe mW level, shared by all generated frequencies [23].The n laser inputs can be produced using pulse shap- ing from a single broadband laser source [24–27]. Giventhe limitation of a photomixer’s total output power, thedevice is an especially attractive solution for THz mix-ing purposes (and not necessarily deexcitation towardslow n (cid:48) ) where the total power is divided up into less fre-quencies. As mentioned in section II, this is the casefor schemes relying on deexcitation lasers. Additionally,the maximum achievable output power rapidly decreasestowards the few THz frequency region rendering the de-vice unfit for the deexcitation purpose below n <
15. Weconclude that, in particular for the THz mixing scheme,photomixers exhibit very attractive characteristics. Fur-thermore the photomixer simply reproduces the beatingin the laser spectrum and can thus also be used as abroadband source.
B. Broadband THz sources
Using a broadband source has the main advantagethat a single device might be able to drive many tran-sitions significantly facilitating the experimental imple-mentation. The obvious drawback, however, is that mostof the power will not be emitted at resonant frequenciesand thus much higher total power would be required todrive the needed transitions. This might lead to signif-icant losses due to ionization [28, 29] even if filters canbe used to reduce this effect. As pointed out earlier,the source output power should ideally be constant overthe exploited range of emitted wavelengths which is moredifficult to implement with a single broadband source.Portable synchrotron [30] or table-top Free ElectronLaser sources [31–34] would be ideal broadband sourceswith intense radiance in the far-infrared region, but thecosts of such apparatus are still prohibitive. A possi-ble alternative is the use of femtosecond mode-lockedlasers to generate very short THz pulses using opticalrectification, surface emitters or photoconductive (Aus-ton) switches. However, we can only use sources withfast repetition rates in order for the spontaneous emis-sion to depopulate all levels. Unfortunately, even thoughphotoconductive switches with mW THz average out-put power exist [35], and THz bandwidth in excess of4 THz with power up to 64 µ W as well as optical-power-to-THz-power conversion efficiencies of ∼ − have beendemonstrated [36], the efficiency drops to ∼ − for fastrepetition rates low femtosecond pulse energies. Thus,if using a standard oscillator providing for instance 1 Waverage power, no more than 10 µ W total output poweris expected [18]. Such sources have been tested to drivetransitions between Rydberg atoms, but with only 10%of the population transfer from the n = 50 initial statesdown to n <
40 [37–39].A simple solution would consist of a blackbody emitterwhich efficiently radiates in the THz range [40]. A 1000 Kblackbody emits in the far infrared region of 0.1-5 THz,with a band radiance of 4 mW/cm which seems perfectlycompatible with the requirements found for the antihy- FIG. 2. Illustration of the experimental caesium beam setup. drogen deexcitation purpose. Such a radiation source hasbeen proposed in order to cool internal degrees of freedomof MgH + molecular ions [41]. Between about 400 and100 cm − , the radiant power emitted by a silicon carbide(Globar) source is as high as any conventional infraredsource, but below 100 cm − , as for Nernst lamps or glow-ers that become transparent below about 200 cm − , theemissivity is low. In the region between ∼ −
10 cm − it is thus customary to use a high-pressure mercury lampwith a spectrum close to a blackbody one of effectivetemperature of 1000-5000 K [30, 40, 42–46]. IV. EXPERIMENTAL CAESIUM TEST SETUP
In order to experimentally assess the potential of thediscussed source types, to evaluate realistic power out-puts, and to study the suitability of the sources forapplication to antihydrogen state mixing and deexcita-tion, we have tested, on a beam of excited Rydberg cae-sium atoms, the narrow- and broadband solution whichseemed most optimal. The reason to use caesium andnot directly hydrogen atoms is mainly due to the factthat, compared to hydrogen, light to manipulate caesiumatoms is much easier to generate and off-the-shelf solu-tions readily exist. However, alkaline Rydberg atoms,such as caesium, have a behavior close to that of hydro-gen.In our experimental setup, illustrated in Fig. 2, a cae-sium effusive beam emitted out of an oven enters a vac-uum chamber. The atoms are excited by a cw diode at852 nm from the 6S / to the 6P / level. A second tun-able pulsed laser (OPO pumped by a Nd:YAG) then ad-dresses the n S or n D Rydberg level. The excitation lasersare sent perpendicular to the beam direction. Two gridsopposing each other perpendicular to the beam directionintroduce an electric field to field ionize the atoms andstudy the population of each ( n, l ) state. The THz radi-ation emitted by a narrowband photomixer outside thechamber can be sent through a THz transparent viewporttowards the excited Cs atoms. Alternatively, a broad-band lamp is mounted inside the chamber in proximity to the measurement region to stimulate a population trans-ferThe caesium state population was studied by applyinga high voltage pulse to the lower grid (cf. Fig. 2, the othergrid was grounded) of the field ionizer surrounding theatomic beam at a given delay time t D with respect tothe laser excitation pulse. The ionizing field was rampedmaking use of an RC circuit with a rise time of 4 µ s. Sinceeach state ionizes at a given electric field strength, thestate distribution can be probed by collecting either theions or electrons from the ionization on a Chevron stackmicro-channel plate (MCP) charge detector [47, 48].We tested a commercial (GaAs Toptica) photomixeracting as a THz source stimulating the 97 GHz transi-tion between the initially excited 36S / state towardsthe 36P / Rydberg state. This transition was cho-sen due to a strong dipole transition, easy laser exci-tation and a well defined field ionization signal. Un-doubtedly, much more cost-effective, convenient and ef-ficient ways to induce a 97 GHz transition would havebeen to use a voltage-controlled oscillator (VCO), semi-conductor (Gunn or IMPATT diode), backward-wave os-cillator or a submillimeter-wave source based on har-monic generation of microwave radiation. However, ourgoal was not to drive specifically this transition, butto demonstrate the use of a photomixer to drive Ry-dberg transitions. This technology allows to create aspectrum of multiple sharp frequencies to simultaneouslydrive many transitions in antihydrogen which ultimatelyresults in a deexcitation of the atoms. In the context ofthis proof-of-principle experiment, mixing of near 852 nmlaser lines from a Ti:Sa laser and a diode laser was usedto produce ∼ µ W THz output power at 97 GHz with aspectral linewidth which reproduces the one of the inputlasers ( < ∼ µ s. A population transfer is clearlyvisible in Fig. 3 and amounts to ∼
15% correspondingto a stimulated transition rate of the order of 10 s − .In theory, the large Cs dipole matrix element (554 . ea for the 36S / → / transition [49]) should lead to amuch faster transition rate of Ω ∼ s − when assum-ing a light intensity of ∼ µ W / cm . The experimentallyobserved lower rate is mainly explained by a transitionbroadening due to large field inhomogeneities in the re-gion traversed by the Cs beam. Indeed, in our geometry,the MCP produces a fringe field between the two field-ionizer plates that can reach tens of V / cm leading to abroadening of tens of GHz for the transition addressed[49]. This measurement demonstrates the first, to ourknowledge, use of a photomixer to stimulate Rydbergtransitions in caesium atoms.Fig. 4 shows results obtained using a globar type (ASB-IR-12K from Spectral Products) lamp which is a siliconnitride emitter mounted in a 1 inch parabolic reflectorthat is small enough to be placed inside the vacuumchamber ∼ t D of the ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ ■■■■■■■■ ■■ ■■■▲▲ ▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲ ▲ ▲▲ ▲▲▲▲▲▲ ▲▲ ▲▲ ▲ ▲ ▲■ without photomixer ▲ with photomixer2.8 3.0 3.2 3.4 3.6 3.8 4.00.00.51.01.52.02.53.0 Time of flight [ μ s ] M C P s i gna l [ a . u . ] FIG. 3. Caesium population transfer from the 36S / to the36P / level. The obtained MCP signal is plotted for case(1) where the photomixer is switched on (triangle) and case(2) where the photomixer is turned off (square). We indi-cate on the x-axis the time reference of the signal to the highvoltage ramp that is applied to the field ionizer grids. TheCs atoms ionize at a given electric field strength and acceler-ate towards the MCP. The ionization rate of the 36P / levelpeaks around ∼ . µ s after the high voltage ramp is started.The detection rate of ions originating from the ionization ofthe 36S / level reaches its maximum approximately 250 nslater. To improve the readability, the signals are averagedover 0 . µ s applied ionizing field ramp with respect to the excita-tion laser was varied to study the population of a givenstate (that ionizes at a given field strength) as a func-tion of time. To probe the population of these states weintegrate the signal in a ∼
200 ns time window aroundthe mean arrival time of the field ionization signal. Thedesired signal can thus be slightly contaminated by theionization signal from nearby states. We compare thelifetimes of the state for stimulated population trans-fer (lamp on) and sole spontaneous emission (lamp off).Fig. 4 shows the results obtained for the 40D / level.This level was chosen because n ∼
40 is close to thehighest level that we would hope to transfer in the caseof antihydrogen [14]. Although the decay curves are non-exponential, we indicate the 1 /e depopulation time thatdecreases from 11 µ s to 3 . µ s using the lamp. To inter-pret this result, we simulate the spontaneous and lightinduced depopulation of the 40D / state within the cae-sium atomic system. Dealing with non-coherent lightsources we place ourselves in the low saturation limit andreduce the optical Bloch equations to a much simpler setof rate equations. The resulting matrix system is nu-merically solved for a few hundred atoms as detailed in[50]. The simulations indicate that the enhancement ofthe decay achieved experimentally is comparable to thesimulation result obtained by implementing a light sourcethat emits an isotropic blackbody spectrum of ∼ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■■ ■ ■ ■ ■ ■●●●●●●●●● ●●●●●●●●●● ●●●●●●●●●■ lamp on ● lamp off0 5 10 15 200.00.20.40.60.81.0 t D [ μ s ] N o r m a li z edpopu l a t i ono f D / FIG. 4. Experimentally measured lifetimes of the caesium40D / level with and without a lamp (globar type). Thetime t D , given on the x-axis, indicates the time delay of thefield ionization ramp with respect to the excitation laser. Weinclude simulation results for a 1100 K blackbody spectrum(gray). To improve the readability the experimental signalsare averaged over 0 . µ s the atoms. In addition, we observed that ∼
50% of theatoms are either excited to higher levels or photoionized[51]. However, we note that filters, such as TPX, PTFEor Teflon [40], can be used to cut out the low (to avoid n → n + 1 transitions) and high (to avoid direct pho-toionization) frequency parts of the spectrum that leadto these effects [51].We note that in the cryogenic environment of an anti-hydrogen experiment the installation of such a high tem-perature lamp in the vicinity of the atoms remains hy-pothetical. However, using transport of THz radiationby, for example, a metallic light pipe is simple and effi-cient [40]. We investigated the transmission efficiency ofthe lamp’s broadband spectrum with a 30 cm long coppertube (diameter: ∼ ≥ .
5% [51]of the radiation.
V. CONCLUSIONS
This work reviewed different methods of generatinglight in the THz region to stimulate the decay of Ry-dberg antihydrogen atoms towards ground state.We commissioned a beamline to study Rydberg popu-lation transfer in alkaline atoms. Cesium atoms are mucheasier to produce than (anti-)hydrogen and are thus idealfor proof-of-principle studies. A ∼
15% population trans-fer within the n = 36 manifold was demonstrated us-ing photomixing at ∼ . n -manifolds [14]. Be-cause antihydrogen is formed (by collisions) in many Ry-dberg levels this mixing and deexcitation requires sev-eral frequencies. The photomixer frequency range of ∼ − ≤ n ≤
30) could be the use of tapered amplifiers,i. e. semiconductor optical amplifiers, or the amplifiedspontaneous emission output of an optical amplifier, asradiation inputs towards the photomixer.A deexcitation of the Cs 40D / was observed usinga blackbody type light source. However, the ionizationfraction for a broadband source lies around ∼
50% andis significantly elevated compared to the use of narrow-band light sources that emit sharp frequencies targetedtowards single n → n − VI. ACKNOWLEDGEMENTS
We dedicate this work to the memory of our co-authorEmiliya Dimova who passed away at the age of 50.This work has been sponsored by the Wolfgang Gen-tner CERN Doctoral Student Program of the GermanFederal Ministry of Education and Research (grant no.05E15CHA, university supervision by Norbert Pietralla).It was supported by the Studienstiftung des DeutschenVolkes and the Bulgarian Science Fund Grant DN 18/14.
VII. AUTHOR CONTRIBUTION STATEMENT
All authors contributed to the work reported in thismanuscript. [1] M. Ahmadi, B. X. R. Alves, C. J. Baker, WilliamBertsche, et al. Antihydrogen accumulation for funda-mental symmetry tests.
Nature Communications , 8:681,Dec 2017.[2] N. Kuroda, S. Ulmer, D. J. Murtagh, S. Van Gorp, et al.A source of antihydrogen for in-flight hyperfine spec-troscopy.
Nature Communications , 5:3089, Jan 2014.[3] G. Gabrielse, R. Kalra, W. S. Kolthammer, R. Mc-Connell, et al. Trapped antihydrogen in its ground state.
Phys. Rev. Lett. , 108:113002, Mar 2012.[4] G. Gabrielse, N. S. Bowden, P. Oxley, A. Speck, et al.Background-free observation of cold antihydrogen withfield-ionization analysis of its states.
Phys. Rev. Lett. ,89(21):213401, Oct 2002.[5] C. Malbrunot, C. Amsler, S. Arguedas Cuendis,H. Breuker, et al. The ASACUSA antihydrogen andhydrogen program: results and prospects.
Philosophi-cal Transactions of the Royal Society A: Mathematical,Physical and Engineering Sciences , 376(2116):20170273,Feb 2018.[6] F. Robicheaux. Atomic processes in antihydrogen ex-periments: a theoretical and computational perspective.
Journal of Physics B: Atomic, Molecular and OpticalPhysics , 41(19):192001, Sep 2008.[7] B. Radics, D. J. Murtagh, Y. Yamazaki, and F. Ro-bicheaux. Scaling behavior of the ground-state antihydro-gen yield as a function of positron density and temper-ature from classical-trajectory monte carlo simulations.
Phys. Rev. A , 90:032704, Sep 2014.[8] S. Jonsell and M. Charlton. Formation of antihydrogenbeams from positron–antiproton interactions.
New Jour- nal of Physics , 21(7):073020, Jul 2019.[9] D. Krasnick´y, G. Testera, and N. Zurlo. Comparison ofclassical and quantum models of anti-hydrogen formationthrough charge exchange.
Journal of Physics B: Atomic,Molecular and Optical Physics , 52(11):115202, May 2019.[10] D. Krasnick´y, R. Caravita, C. Canali, and G. Testera.Cross section for Rydberg antihydrogen production viacharge exchange between Rydberg positroniums and an-tiprotons in a magnetic field.
Phys. Rev. A , 94(2):022714,Aug 2016.[11] M. Doser, C. Amsler, A. Belov, G. Bonomi, et al. Ex-ploring the WEP with a pulsed cold beam of antihydro-gen.
Classical and Quantum Gravity , 29(18):184009, Aug2012.[12] Edward S. Chang. Radiative lifetime of hydrogenic andquasihydrogenic atoms.
Phys. Rev. A , 31:495–498, Jan1985.[13] T. Top¸cu and F. Robicheaux. Radiative cascade of highlyexcited hydrogen atoms in strong magnetic fields.
Phys.Rev. A , 73(4):043405, Apr 2006.[14] T. Wolz, C. Malbrunot, M. Vieille-Grosjean, andD. Comparat. Stimulated decay and formation of an-tihydrogen atoms.
Phys. Rev. A , 101:043412, Apr 2020.[15] T. F. Gallagher.
Rydberg Atoms . Cambridge Monographson Atomic, Molecular and Chemical Physics. CambridgeUniversity Press, 1994.[16] D. Comparat and C. Malbrunot. Laser stimulated deex-citation of Rydberg antihydrogen atoms.
Phys. Rev. A ,99:013418, Jan 2019.[17] P. Latzel, F. Pavanello, S. Bretin, M. Billet, et al. High ef-ficiency UTC photodiode for high spectral efficiency THz links. In , pages1–2, Aug 2017.[18] M. Hangyo. Development and future prospects of tera-hertz technology.
Japanese Journal of Applied Physics ,54(12):120101, Dec 2015.[19] S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A.G.Davies, et al. The 2017 terahertz science and technol-ogy roadmap.
Journal of Physics D: Applied Physics ,50(4):043001, Jan 2017.[20] K. Zhong, W. Shi, D. Xu, P. Liu, et al. Optically pumpedterahertz sources.
Science China Technological Sciences ,60(12):1801–1818, Jun 2017.[21] T. Els¨asser, K. Reimann, and M. Woerner.
Concepts andApplications of Nonlinear Terahertz Spectroscopy . Mor-gan & Claypool Publishers, Feb 2019.[22] J. Ahn, A. V. Efimov, R. D. Averitt, and A. T. Taylor.Terahertz waveform synthesis via optical rectification ofshaped ultrafast laser pulses.
Optics Express , 11:2486,Oct 2003.[23] S. Preu, G. H. D¨ohler, S. Malzer, L. J. Wang, et al. Tun-able, continuous-wave Terahertz photomixer sources andapplications.
Journal of Applied Physics , 109(6):061301–061301, Mar 2011.[24] Y. Liu, S. Park, and A. M. Weiner. Terahertz wave-form synthesis via optical pulse shaping.
Selected Topicsin Quantum Electronics, IEEE Journal of , 2(3):709–719,Sep 1996.[25] A. J. Metcalf, V. R. Supradeepa, D. E. Leaird, A. M.Weiner, et al. Fully programmable two-dimensional pulseshaper for broadband line-by-line amplitude and phasecontrol.
Optics express , 21(23):28029–28039, Nov 2013.[26] M. Hamamda, P. Pillet, H. Lignier, and D. Comparat.Ro-vibrational cooling of molecules and prospects.
Jour-nal of Physics B: Atomic, Molecular and Optical Physics ,48(18):182001, Aug 2015.[27] A. I. Finneran, J. T. Good, D. B. Holland, P. B. Car-roll, et al. Decade-spanning high-precision terahertz fre-quency comb.
Phys. Rev. Lett. , 114(16):163902, Apr2015.[28] I. L. Glukhov, E. A. Nekipelov, and V. D. Ovsiannikov.Blackbody-induced decay, excitation and ionization ratesfor rydberg states in hydrogen and helium atoms.
Jour-nal of Physics B: Atomic, Molecular and Optical Physics ,43(12):125002, Jun 2010.[29] C. Seiler, J. A. Agner, P. Pillet, and F. Merkt. Radiativeand collisional processes in translationally cold samplesof hydrogen rydberg atoms studied in an electrostatictrap.
Journal of Physics B: Atomic, Molecular and Op-tical Physics , 49(9):094006, Apr 2016.[30] P. R. Griffiths and C. C. Homes.
Instrumentation forFar-Infrared Spectroscopy . Wiley Online Library, 2006.[31] S. M. Hooker. Developments in laser-driven plasma ac-celerators.
Nature Photonics , 7(10):775–782, Sep 2013.[32] Y. Shibata, K. Ishi, S. Ono, Y. Inoue, et al. Broad-band free electron laser by the use of prebunched electronbeam.
Phys. Rev. Lett. , 78(14):2740, Apr 1997.[33] K. Nakajima. Laser-driven electron beam and radia-tion sources for basic, medical and industrial sciences.
Proceeding of the Japan Academy, Series B , 91:223–245,2015.[34] A. Wetzels, A. G¨urtler, L. D. Noordam, and F. Ro-bicheaux. Far-infrared Rydberg-Rydberg transitions ina magnetic field: Deexcitation of antihydrogen atoms.
Phys. Rev. A , 73(6):062507, Jun 2006.[35] E. R. Brown. Milliwatt thz average output power froma photoconductive switch. In
Infrared, Millimeter andTerahertz Waves, 2008. IRMMW-THz 2008. 33rd Inter-national Conference on , pages 1–2. IEEE, 2008.[36] R. J. B. Dietz, B. Globisch, M. Gerhard, A. Velau-thapillai, et al. 64 µ W pulsed terahertz emission fromgrowth optimized InGaAs/InAlAs heterostructures withseparated photoconductive and trapping regions.
AppliedPhysics Letters , 103(6):061103, Aug 2013.[37] P. K. Mandal and A. Speck. Half-cycle-pulse-train in-duced state redistribution of rydberg atoms.
Phys. Rev.A , 81(1):013401, Oct 2010.[38] T. Kopyciuk. Deexcitation of one-dimensional Rydbergatoms with a chirped train of half-cycle pulses.
PhysicsLetters A , 374(34):3464–3467, Jul 2010.[39] A. Takamine, R. Shiozuka, and H. Maeda. Population re-distribution of cold rydberg atoms. In
Proceedings of the12th International Conference on Low Energy AntiprotonPhysics (LEAP2016) , page 011025, Nov 2017.[40] E. Br¨undermann, H. H¨ubers, and M. F. Kimmitt.
Tera-hertz Techniques , volume 151. Springer, 2012.[41] I. S. Vogelius, L. B. Madsen, and M. Drewsen. Rotationalcooling of molecules using lamps.
Journal of Physics B ,37:4571–4574, Nov 2004.[42] M. W. P. Cann. Light sources in the 0.15–20- µ spectralrange. Applied optics , 8(8):1645–1661, Aug 1969.[43] W. L. Wolfe and G. J. Zissis.
The infrared handbook ,volume 1. Spie Press, 1978.[44] M. F. Kimmitt, J. E. Walsh, C. L. Platt, K. Miller, et al.Infrared output from a compact high pressure arc source.
Infrared Physics and Technology , 37:471–477, Jun 1996.[45] H. Buijs.
Incandescent Sources for Mid-and Far-InfraredSpectrometry . Wiley Online Library, 2002.[46] M. Abo-Bakr, J. Feikes, K. Holldack, P. Kuske, et al.Brilliant, Coherent Far-Infrared (THz) Synchrotron Ra-diation.
Phys. Rev. Lett. , 90(9):094801–+, Mar 2003.[47] T. W. Ducas, W. P. Spencer, A G. Vaidyanathan, W. H.Hamilton, et al. Detection of far-infrared radiation usingrydberg atoms.
Appl. Phys. Lett. , 35(5):382–384, Aug1979.[48] L Hollberg and JL Hall. Measurement of the shift ofRydberg energy levels induced by blackbody radiation.
Phys. Rev. Lett. , 53(3):230, Jul 1984.[49] N. ˆSibali´c, J. D. Pritchard, Adams C. S., and K. J.Weatherill. ARC: An open-source library for calculatingproperties of alkali Rydberg atoms.
Computer PhysicsCommunications , 220:319 – 331, 2017.[50] D. Comparat. Molecular cooling via Sisyphus processes.
Phys. Rev. A , 89(4):43410, Apr 2014.[51] M. Vieille Grosjean.