We present experimental observation of electromagnetically induced
transparency (EIT) on a single macroscopic artificial "atom" (superconducting
quantum system) coupled to open 1D space of a transmission line. Unlike in a
optical media with many atoms, the single atom EIT in 1D space is revealed in
suppression of reflection of electromagnetic waves, rather than absorption. The
observed almost 100 % modulation of the reflection and transmission of
propagating microwaves demonstrates full controllability of individual
artificial atoms and a possibility to manipulate the atomic states. The system
can be used as a switchable mirror of microwaves and opens a good perspective
for its applications in photonic quantum information processing and other
fields

A. A. Abdumalikov

A. M. Zagoskin

J. S. Tsai

M. O. Scully

O. Astafiev

Y. Nakamura

Yu. A. Pashkin

English

arXiv

Crossref

Electromagnetically Induced Transparency on a Single Artificial Atom

We present experimental observation of electromagnetically induced transparency (EIT) on a single macroscopic artificial “atom” (superconducting quantum system) coupled to open 1D space of a transmission line. Unlike in an optical media with many atoms, the single-atom EIT in 1D space is revealed in suppression of reflection of electromagnetic waves, rather than absorption. The observed almost 100% modulation of the reflection and transmission of propagating microwaves demonstrates full controllability of individual artificial atoms and a possibility to manipulate the atomic states. The system can be used as a switchable mirror of microwaves and opens a good perspective for its applications in photonic quantum information processing and other fields

A.A. Abdumalikov (7170545)

O.V. Astafiev (7170542)

Alexandre Zagoskin (1251504)

Yu A. Pashkin (7170548)

Y. Nakamura (2711890)

J.S. Tsai (7170554)

Loughborough University Institutional Repository

Electromagnetically Induced Transparency on a Single Artificial AtomA.A. Abdumalikov, Jr.,1,* O. Astafiev,1,2 A.M. Zagoskin,3 Yu. A. Pashkin,1,2,† Y. Nakamura,1,2 and J. S. Tsai1,21RIKEN Advanced Science Institute, Wako, Saitama 351-0198, Japan2NEC Nano Electronics Research Laboratories, Tsukuba, Ibaraki 305-8501, Japan3Department of Physics, Loughborough University, Loughborough, LE11 3TU Leicestershire, United Kingdom(Received 23 February 2010; published 11 May 2010)We present experimental observation of electromagnetically induced transparency (EIT) on a singlemacroscopic artificial ‘‘atom’’ (superconducting quantum system) coupled to open 1D space of atransmission line. Unlike in an optical media with many atoms, the single-atom EIT in 1D space isrevealed in suppression of reflection of electromagnetic waves, rather than absorption. The observedalmost 100% modulation of the reflection and transmission of propagating microwaves demonstrates fullcontrollability of individual artificial atoms and a possibility to manipulate the atomic states. The systemcan be used as a switchable mirror of microwaves and opens a good perspective for its applications inphotonic quantum information processing and other fields.DOI: 10.1103/PhysRevLett.104.193601 PACS numbers: 42.50.Gy, 85.25.jCoherent evolution of atomic population under resonantcoherent drive, known as Rabi oscillations in two-levelatoms [1], leads to quantum interference phenomena in amore complicated case of a multilevel atom. In particu-lar, in a three-level atom driven by two resonant waves[Fig. 1(a)], the destructive interference between differentexcitation pathways cancels out the population of one ofthe atomic states effectively turning the atom to the ‘‘darkstate.’’ This leads to the suppression of transition from the‘‘dark state,’’ revealed in the elimination of light absorptionby an optical media, electromagnetically induced trans-parency (EIT) [1–3]. Scaling the media down to a singleatom perfectly coupled to the incident waves leads toqualitatively new properties of EIT: the waves are scatteredrather than absorbed. However, the strong interaction be-tween the spatial electromagnetic modes and natural atoms(molecules, quantum dots) is very difficult to realize inpractice [4–9]. Recently, the strong ‘‘atom’’-field interac-tion has been achieved by confining the waves in the 1Dtransmission line efficiently coupled to an artificial three-level atom [10]—a superconducting quantum circuit. In aseries of experiments [11–19] many fundamental quantumeffects known from quantum optics, atomic physics andnuclear magnetic resonance have been reproduced usingsuperconducting quantum circuits. However, most of thoseworks focused on the two lowest levels. EIT related phe-nomena in superconducting circuits was theoreticallystudied in Ref. [20].In a few recent experiments multilevel structure ofsuperconducting quantum circuits has been used to dem-onstrate Autler-Townes splitting and coherent populationtrapping [21–23]. Baur et al. observed Autler-Townessplitting in a three-level quantum system coupled to acavity using dispersive measurement. In Refs. [22,23],only level occupations were measured. In neither of theseexperiments was direct transmission of probe fieldmeasured.Our artificial atom is a macroscopic size (>1 m)superconducting loop interrupted by four Josephson junc-tions, which has been used as a two-level system or a fluxqubit [13,24] in earlier experiments. We exploit three low-controlprobe I0123 1.00.80.60.411.210.610.811.0ωp/2π (GHz)|t|24- 0 42-δΦ/Φ0 ×103|t/t0|35.234.634.835.0ωc/2π (GHz)24- 0 42-δΦ/Φ0 ×1031.00.80.60.4(b)(a)(c) (d)|t/t0|2.01.61.20.824.624.024.224.4ωc/2π (GHz)24- 0 42-δΦ/Φ0 ×103ΩcΩprI0tI0FIG. 1 (color online). Three-level cascade system.(a) Schematic of the three-level cascade atom used to produceelectromagnetically induced transparency—the physical phe-nomena for the quantum switch. Transmission of a weak prop-agating wave at the frequency !p close to the transitionfrequency !21 is controlled by another field coupling states j2iand j3i. The corresponding Rabi drive amplitudes are denoted byc and p, respectively. (b) Transmission spectrum for j1i $j2i transition. (c) Spectrum of j2i $ j3i transition. The spec-troscopy signal appears only around the degeneracy point. Thetransition frequency between states j2i and j3i at the degeneracy( ¼ 0) is !32 ¼ 24:465 GHz. (d) Spectrum of j1i $ j3itransition. At the degeneracy point  ¼ 0 the transition isprohibited, and the spectroscopy signal vanishes indicating thatthe cascade system is realized.PRL 104, 193601 (2010) P HY S I CA L R EV I EW LE T T E R Sweek ending14 MAY 20100031-9007=10=104(19)=193601(4) 193601-1  2010 The American Physical Societyest states jii (i ¼ 1, 2, 3) with energies @!i, schematicallyrepresented in Fig. 1(a). The device parameters are de-signed such that all relevant transition frequencies of thethree-level system !ij ¼ !i !j (i > j) fall within thefrequency band of our experimental setup limited by40 GHz. The atomic levels are controlled by the externalmagnetic flux thread through the loop  ¼ 0=2þ ,where0 is the flux quantum and  is the deviation from0=2. The loop is inductively coupled to a transmissionline (open 1D space) via a mutual kinetic inductance M[25]. At the degeneracy point  ¼ 0 the atom has aladder-type energy level structure. Because of symmetryof eigenstate wave functions j1i $ j2i and j2i $ j3i tran-sitions are allowed, while the transition j1i $ j3i is for-bidden. The coplanar transmission line with thecharacteristic impedance Z ’ 50  was made by pattern-ing a gold film deposited on a silicon substrate. In themiddle of the chip, the central conductor of the waveguideis narrowed and replaced by an aluminum strip. Our ex-periment is performed in a dilution refrigerator at a tem-perature of 40 mK.In the rotating wave approximation, the three-level sys-tem under the drive of two fields with frequencies !p ¼!21 þ !p and !c ¼ !32 þ !c, where !p and !cpresent small detunings from corresponding resonances!21 and !32, is described by the HamiltonianHa ¼ @ð!p22 þ ð!p þ !cÞ33Þ @p2ð21 þ 12Þ þc2 ð32 þ 32Þ: (1)Here ij ¼ jiihjj is the atomic projection or transitionoperator, and @p ¼ 21Ip and @c ¼ 32Ic are theprobe and control dipole interaction energies for the tran-sitions j2i $ j1i and j3i $ j2i, respectively. Under theinfluence of the two fields in the transmission line withthe actual current values given by Re½Ipð0; tÞ ¼ Ip cos!ptand Re½Icð0; tÞ ¼ Ic cos!ct. Here we assume that ourpointlike atom is situated at x ¼ 0 and the waves frommicrowave sources Ipðx; tÞ ¼ Ip expðikpx i!ptÞ andIcðx; tÞ ¼ Ic expðikcx i!ctÞ propagate in the transmis-sion line. The dipole matrix element can be presented inthe form ij ¼ ijMiPC with the dimensionality of a mag-netic flux, where ij is the dimensionless matrix element(0  ij  1), M is the line-atom mutual inductance, andiPC is the amplitude of the persistent current in the loop.The atomic dynamics is described by the Markovianmaster equation for the density matrix  ¼ ijjiihjj,_ ¼ ði=@Þ½H; þ L½; (2)with the Lindblad termL½ ¼ 3233ð33 þ 22Þ þ 2122ð22 þ 11ÞþXijijijij: (3)Here ij ¼ ji is the damping rate of the off-diagonalterms (dephasing) and ij is the relaxation rate betweenthe levels jii and jji (i > j). In the ladder-type three-levelatom the j3i ! j1i transition is omitted, since 31 ¼ 0. Inour case the condition (@!ij  kBT) is fulfilled and theabsence of thermal excitations (12 ¼ 0 and 23 ¼ 0) isguaranteed.One can show that the atom interacting only with con-tinuummodes of 1D open space generates a scattered waveat the probe frequency [10]Iscðx; tÞ ¼ i @2121 h12ieikjxji!pt; (4)where hiji ¼ tr½ij ¼ ji can be straightforwardlyfound in the stationary conditions ( _ ¼ 0), when the mas-ter equation reduces to a set of linear algebraic equations.The transmission coefficient found as a ratio of the result-ing current Ipðx; tÞ þ Iscðx; tÞ (at x > 0) to the incident oneIpðx; tÞ and for weak probe drive p  21, the trans-mission coefficient ist ¼ 1 212ð21  i!pÞ þ 2c2ð31i!pi!cÞ: (5)The complex transmission coefficient t is monitoredusing a vector network analyzer in the frequency rangefrom 5 to 13 GHz. Measuring t versus probing frequency!p and the magnetic flux , the resonant transitionfrequency !21 is revealed as a sharp dip in jtj [dark linein Fig. 1(b)]. By fitting !21 we find that the minimalfrequency !21=2 reaches 10.165 GHz at  ¼ 0, andthe persistent current in the loop is iPC ¼ 200 nA. Nextanalyzing the spectroscopy line shape of jtj at  ¼ 0, therelaxation and dephasing rates are found to be 21 ¼ 6:9107 s1 (21=2 ¼ 11 MHz) and 21 ¼ 4:5 107 s1(21=2 ¼ 7:2 MHz) [10]. Nonradiative emission insuch systems is expected to be negligible with a corre-sponding relaxation rate less than 106 s1, measured inearlier experiments [26]. Therefore, we conclude that therelaxation is caused solely by the quantum noise of open1D space defined by the rate 21 ¼ @!21ðMiPCÞ2=ð@2ZÞand derive the mutual inductance between the loop andthe transmission line to be M  12 pH.The transition frequencies!31 and!32 cannot be probedin the direct transmission, since they exceed the highfrequency cutoff (13 GHz) of the cryogenic amplifier. Tofind themwe use two-tone spectroscopy: the frequency of aweak probe tone!p is adjusted to!21 [found from the datashown in Fig. 1(b)], where the transmission t0 is minimal(jt0j< 1). Next, the transmission t is continuously moni-tored, while the second (control) tone frequency !c isswept. When !c is in resonance with the correspondingtransitions, total population j1i and j2i is decreased and,therefore, jtj is enhanced, revealing the spectral lines in theplot of jt=t0j. Figures 1(c) and 1(d) show traces of thePRL 104, 193601 (2010) P HY S I CA L R EV I EW LE T T E R Sweek ending14 MAY 2010193601-2spectroscopy lines for !32 and !31, respectively. Becauseof the symmetry of eigenstate wave functions, the selectionrule in our system prohibits transitions between states j1iand j3i at  ¼ 0, which is seen in Fig. 1(c) as thevanishing spectroscopy signal. At the same time, the ma-trix elements for j1i to j2i and j2i to j3i transitions reachtheir maximum. Thus at the degeneracy point, we have aladder-type three-level quantum system [1], schematicallyrepresented in Fig. 1(a), with two allowed and one forbid-den transitions. The enhancement of transmission (sup-pression of reflection) in Fig. 1(c) is already a signatureof the single-atom EIT, which we study in detail at  ¼0.Electromagnetic response of the single atom is naturallycharacterized by polarizability 	 (rather than susceptibilityused to characterize the optical response of macroscopicmedia). The polarizability is a ratio of the atomic dipolemoment to the excitation field (in our case defined as theinduced magnetic flux in the loop to the incident wavecurrent amplitude). The atom scatters waves [10] and thepolarizability is related to the reflection and the transmis-sion according to 	 / ir ¼ ið1 tÞ. The polarizability canbe presented as 	 ¼ 	0 þ i	00 with the real and imaginaryparts 	0 and 	00 related to dispersion and reflection, re-spectively. Figure 2(a) demonstrates transmission ReðtÞ /1 	00 for different amplitudes c (associated with ab-sorption in EIT for media), while Fig. 2(b) shows disper-sion curves of ImðtÞ / 	0. The probing amplitude in themeasurements is fixed top=2 ’ 2 MHz. In the absenceof control field (black curves in Fig. 2), the wave is stronglyreflected, exhibiting the Lorentzian dip in ReðtÞ, whileImðtÞ follows the typical anomalous dispersion curve inthe vicinity of the resonant transition. With increasingcontrol field amplitude c, the dip is split, and at thestrongest drive (c=2 ¼ 44 MHz) the dip is completelysuppressed, exhibiting full transparency at the exact reso-nance (!p ¼ 0) and a dispersion curve typical for EIT inFig. 2(b). Figures 2(c) and 2(d) show our calculations ofReðtÞ and ImðtÞ, respectively, with 31 ¼ 4:3 107 s1(31=2 ¼ 6:9 MHz), which is comparable to 21. Inatomic physics, the transmission window much narrowerthan the absorption dip appears already for weak controlamplitude (c  21) because of small dephasing be-tween levels j1i and j3i (31  21) [3].Figure 3(a) summarizes the data of Figs. 2(a) and 2(b),showing the power transmission coefficient T ¼ jtj2 as afunction of control field amplitude c. The splitting at thestrong drive is known as the Autler-Townes splitting [27].It arises due to Rabi splitting of levels j2i and j3i. In thepresent experiments we could induce larger than 100 MHzsplitting. Figures 2 and 3(a) demonstrate that the trans-mission strongly depends on the control field c, and,therefore, the latter can be used to control transmissionand reflection for the probing wave. However, all the powercan be reflected or transmitted only in extreme cases ofc ¼ 0 or c  31, respectively. The power transmis-sion T at the exact probing wave resonance (!p ¼ 0) ispresented in Fig. 3(b). The transmitted wave extinctionexhibits contrast of 96%, which demonstrates that theartificial atom can be used as a highly efficient directionalswitch (or mirror) for propagating waves. The power ex-tinction is close to the ideal case of 100%, which ispossible in the absence of pure dephasing for the probetransition (21 ¼ 21=2) and if all the incident powerinteracts with the atom. In such a case the power trans-mission is presented by the simple formulaT ¼2c22131 þ2c2: (6)1.8 MHz7 MHz12 MHz22 MHz44 MHz1.00.80.60.40.2Re(t)0.40.20.0-0.2-0.4Im(t)-40 -20 0 20 40δωp/2π (MHz)-40 -20 0 20 40δωp/2π (MHz)(b)(a)1.00.80.60.40.2Re(t)-40 -20 0 20 40δωp/2π (MHz)-40 -20 0 20 40δωp/2π (MHz)0.40.20.0-0.2-0.4Im(t)(d)(c)FIG. 2 (color online). Transmission coefficient near the probewave resonance (!p ¼ 0). (a) and (b) are real and imaginaryparts of the probe signal transmission coefficient at the differentcontrol field amplitudes c, specified in (b). The curves showtypical dispersion for EIT. (c) and (d) present calculations of realand imaginary parts for the probe signal transmission coefficientfor the same set of c as in (a) and (b).0.00.250.50.751.0T4 10 40 100Ωc/2π (MHz)96%ExpTheory(b)4 10 40 100Ωc/2π (MHz)50250-25-50δωp/2π (MHz)(a)0.00.250.50.751.0TFIG. 3 (color online). Quantum switch operation. (a) Powertransmission coefficient T vs control field amplitude c andprobe frequency. The single resonant dip in the transmission issplit into two under the large control field amplitudes. (b) T forresonant probe signal vs control field amplitude. The experimen-tally measured T is presented by red circles, and the black line iscalculated jtj2 from Eq. (5). The achieved contrast in the trans-mitted power is 96%.PRL 104, 193601 (2010) P HY S I CA L R EV I EW LE T T E R Sweek ending14 MAY 2010193601-3The black curve in Fig. 3(b) shows the calculation of Tfrom Eq. (5) as jtj2 for our case of weak pure dephasing,which slightly deviates from Eq. (6).In conclusion, we have demonstrated the operation of aquantum switch for propagating waves, which allows thepropagating waves to be fully transmitted or backscattered.The experiment suggests interesting applications in pho-tonics and optical quantum computation. It also demon-strates the possibility of controlling individual atomscoupled to a 1D transmission line, which can be used,e.g., for photonic quantum information processing [28].This work was supported by MEXT KAKENHI‘‘Quantum Cybernetics’’ project.*abdumalikov@zc.jp.nec.comOn leave from Physical-Technical Institute, Tashkent100012, Uzbekistan.†On leave from Lebedev Physical Institute, Moscow119991, Russia.[1] M.O. Scully and M. S. Zubairy, Quantum Optics(Cambridge University Press, Cambridge, U.K., 1997).[2] S. E. Harris, J. E. Field, and A. Imamoglu, Phys. Rev. Lett.64, 1107 (1990).[3] M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev.Mod. Phys. 77, 633 (2005).[4] I. Gerhardt, G. Wrigge, P. Bushev, G. Zumofen, M. Agio,R. Pfab, and V. Sandoghdar, Phys. Rev. Lett. 98, 033601(2007).[5] G. Wrigge, I. Gerhardt, J. Hwang, G. Zumofen, and V.Sandoghdar, Nature Phys. 4, 60 (2008).[6] M.K. Tey, C. Zilong, S. A. Aljunid, B. Chng, F. Huber, G.Maslennikov, and C. 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Electromagnetically induced transparency on a single artificial atom

We present experimental observation of electromagnetically induced transparency (EIT) on a single macroscopic artificial "atom'' (superconducting quantum system) coupled to open 1D space of a transmission line. Unlike in an optical media with many atoms, the single-atom EIT in 1D space is revealed in suppression of reflection of electromagnetic waves, rather than absorption. The observed almost 100% modulation of the reflection and transmission of propagating microwaves demonstrates full controllability of individual artificial atoms and a possibility to manipulate the atomic states. The system can be used as a switchable mirror of microwaves and opens a good perspective for its applications in photonic quantum information processing and other fields

Abdumalikov, A. A.

Astafiev, O.

Zagoskin, A. M.

Pashkin, Yuri

Nakamura, Y.

Tsai, J. S.

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Electromagnetically induced transparency on a single artificial atom

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