Single artificial-atom lasing
O. Astafiev1,2, K. Inomata2, A. O. Niskanen3,4, T. Yamamoto1,2,3, Yu. A. Pashkin1,2, Y.
Nakamura1,2,3 & J. S. Tsai1,2,3
1NEC Nano Electronics Research Laboratories. Tsukuba, Ibaraki, 305-8501, Japan
2The Institute of Physical and Chemical Research (RIKEN), Wako, Saitama 351-0198,
3CREST-JST, Kawaguchi, Saitama 332-0012, Japan
4VTT Technical Research Center of Finland, Sensors, POB 1000, 02044 VTT, Finland
Solid-state superconducting circuits1-3 are versatile systems in which quantum
states can be engineered and controlled. Recent progress in this area has opened up
exciting possibilities for exploring fundamental physics as well as applications in
quantum information technology; in a series of experiments4-8 it was shown that
such circuits can be exploited to generate quantum optical phenomena, by designing
superconducting elements as artificial atoms that are coupled coherently to the
photon field of a resonator. Here we demonstrate a lasing effect with a single
artificial atom—a Josephson-junction charge qubit9—embedded in a
superconducting resonator. We make use of one of the properties of solid-state
artificial atoms, namely that they are strongly and controllably coupled to the
resonator modes. The device is essentially different from existing lasers and masers;
one and the same artificial atom excited by current injection produces many
Conventional lasers and masers consist of many atoms that are weakly coupled to a
cavity owing to the tiny size of natural atoms. Nevertheless, by using a tightly confined
cavity mode, coherent interaction of a single atom and the cavity can be achieved: the
atom-cavity interaction time becomes shorter than the photon lifetime or the atom
coherence time10, 11. Such a strong coupling regime results in a qualitatively new feature:
the vanishing of the pumping threshold that has been experimentally realized in single-
atom masers and lasers12, 13. On the other hand, quantum systems with artificial atoms
allow one to easily make the interaction time much shorter than the coherence time, as it
has been demonstrated recently4-6,14,15. Furthermore, controllable interaction with a single
cavity mode together with a fast mechanism of population inversion gives a possibility to
realize a lasing regime with many photons generated by one and the same atom13, 16, 17.
In this work we demonstrate lasing action in a maser operation based on a single
Josephson-junction charge qubit with a population inversion mechanism provided by
single-electron tunnelling events18. Alternative lasing schemes with superconducting
qubits have been discussed elsewhere. 19, 20.
The artificial-atom maser consists of a resonator and a charge qubit coupled to it
(Fig. 1). We fabricate a transmission-type half-wavelength coplanar-waveguide resonator
using a 200-nm thick Nb film (Fig. 1c). It has a bare resonance frequency 0/2 = 9.899
GHz and a quality factor Q = 7.6103. The corresponding photon decay rate is /2 =
1.3 MHz. The qubit is fabricated by three-angle shadow evaporation of Al close to the
end of the resonator, where the electric field is nearly maximal. The qubit9 is well
described by two charge states, |0 and |2, differing by one Cooper pair (consisting of
two electrons) in the island, and is characterized by the Josephson energy EJ and the
single-electron charging energy EC. The electrostatic energy difference = 4 EC (ng- 1)
between the two states is controlled by the normalized gate charge ng = Cg Vg/e, where Vg
is the gate voltage, Cgthe gate capacitance and e the electron charge. The qubit
eigenenergy follows E =
(top right panel of Fig. 1d). As the qubit is coupled
to the resonator through the electric field (a+ + a, where a+ and a are the photon creation
and annihilation operators, respectively), the hamiltonian of the qubit-resonator system
The first term represents the qubit; z and x are the Pauli matrices. The second term
describes the resonator. The interaction between the qubit and the resonator gives the
third term, and is characterized by the coupling strength g0. The value of g0/2 is found to
be 80 MHz from fitting the dispersion curve observed in the transmission through the
resonator when the qubit is biased at = 0 (Fig. 2a).
To create population inversion in the qubit we introduce a drain electrode
connected to the island via a tunnel junction with the resistance Rb of 1.0 M (Figs. 1a,
b). The drain electrode is voltage biased at a voltage Vb above (2+EC)/e, which is
required to extract two electrons from the island by breaking a Cooper pair (where is
the superconducting gap energy; /h 55 GHz)21, 22. As a result, |2 decays into |0 via
two sequential single-electron tunnelling events in the incoherent process |2 |1 |0
with rates 21, 10 (eVb EC)/e2Rb(positive sign for the former), respectively (bottom
left panel of Fig. 1d). Therefore, the ‘atom’ is pumped into |0 state regardless of the sign
of . At = 0, a Cooper pair tunnels across the Josephson junction from the ground to the
island (|0 |2) without changing its energy. Thus, the so-called Josephson-
quasiparticle (JQP) cycle involving the three charge states continues and results in a
pronounced current peak21,22. For >> EJ, the upper eigenstate of the qubit is nearly the
|0 state, and the single-electron tunnelling process creates population inversion with an
effective rate = 2110/(21+10). For Vb = 0.65 mV used in the measurement below,
2.0109 s-1 ( /2 320 MHz) which is much larger than .
When E is adjusted to 0the energy quantum of the qubit is transferred into the
resonator as a photon, accompanied by a Cooper pair tunnelling across the Josephson
junction (|0, N |2, N+1; |n, N represents a state with n excess electrons in the qubit
island and N photons in the resonator). Completed by the pumping mechanism |2,
N+1 |1, N+1 |0, N+1, the photon-assisted JQP cycle proceeds repeatedly with
increasing N, and N reaches the balance between the photon generation and the loss of the
resonator. The coupling between |0, N and |2, N+1 states is enhanced by a factor of
; the photon field stimulates the photon generation process, which is analogous to
stimulated emission in conventional lasers. However, in our case the photons are
generated by one and the same atom. In conventional lasers, the ratio of spontaneous
decay rate into the lasing mode to the total spontaneous decay rate is very low. Therefore,
high pumping rate (above lasing threshold) is required to achieve lasing. However in our
system, a single atom efficiently coupled to a single-mode cavity with close to unity,
the threshold no longer exists and lasing takes place at any weak pumping rate13, 16.
In Fig. 2b, emission power spectral density from the resonator (upper panel) is
shown together with the current through the qubit (lower panel) as a function of . The
observed current peak at =0 is due to the JQP process. On the right slope of the JQP
peak ( > 0; the emission side), two small current peaks (Ip 0.1 nA above JQP peak)
appear. Correspondingly, we observe strong emission shown as two “hot spots” in the
upper panel. The position of the first current peak and the hot spot corresponds to /2 ~
72 GHz. Although the hot spot is rather broad, it is located consistently with the
condition E = 0 ( =8.3 GHz). (Although the emission takes place in a wide range of
the magnetic flux , the data shown here is obtained at = 0.38 0 (0 is the flux
quantum), where EJ /h 5.4 GHz). Because of finite , the effective coupling strength at
the resonance is reduced to g/2 = (g0/2)(EJ/0) 44 MHz.) One possible
interpretation of the presence of the second hot spot is the two-photon resonance18
expected at = 19 GHz. Note that the emission takes place only when the drain electrode
is biased in the range 0.57 mV Vb 0.71 mV, where the JQP cycle is the dominant
current carrying process. Note also that on the absorption side, < 0, the microwave de-
amplification is expected at E = 0 and is indeed observed, though it is not shown
Figure 2c shows the emission spectrum at one of the hot spots. The frequency of the
intense emission is shifted by ~ 0.7 MHz from the resonator frequency. The emission
peak is unstable, showing low-frequency fluctuations, which can be attributed to the low
frequency charge noise. However, it is roughly confined within the envelope drawn by
the black curve. The total emission power within the envelope is estimated to be W =
710-16 W, which corresponds to N = 2 (W/0)/ 30 photons in the resonator. (The
factor 2 comes from equal probability for the photons to escape from each end of the
resonator: the number 30 may be underestimated, as the resonator internal loss is not
accounted for.) The large number of photons accumulated in the single-mode resonator
indicates lasing effect, together with the linewidth narrower than as well as 21.
However, the linewidth is still much wider than the quantum limit given by the
Schawlow-Townes formula23/(2N) (of order of 210 kHz), which means that it is
broadened by some other mechanism, e.g., charge fluctuations. The -factor is estimated
as a ratio of photon escape rate over the photon assisted Cooper-pair tunnelling rate >
(N)/(Ip/2e) = 0.4. It supports our picture of high lasing efficiency.
To additionally prove the lasing action of our device, we study the amplification of
an external microwave. Figure 3a shows the normalized power and phase of coherent
radiation output from the resonator. The blue curves show an ordinary transmission
through the resonator when the qubit is biased away from the hot spots, and, as expected,
the amplitude exhibits a lorentzian shape. The red curve demonstrates amplification of
the drive microwave: at the hot spots, the transmission peak is enhanced on the low-
frequency side of the bare resonant peak and slightly shifted towards lower frequencies in
respect to the emission peak. At frequency drive /2 ~ – 0.6 MHz (drive drive- 0),
the amplification switches to attenuation accompanied by the phase drop. One possible
interpretation of the frequency shift and the phase drop in Figs 2c and 3a is that they are
signatures of qubit-resonator coupling g(N+1)1/2 that makes the system non-linear in
photon fields N1/2. The resonance frequency and consequently the amplification and
emission peaks are expected to split by approximately g/2N1/2. The observed
amplification peak is shifted by ~ - 1 MHz, which is of the order of the expected value.
However, the peaks shifted to positive frequencies are not observed. The phase shift
accompanying an amplification peak of a narrow band amplifier should also be
additionally affected by the nonlinear term ~N-1/2and therefore drops on the right slope of
the amplification peak, where N is suppressed.
Next we study emission spectrum under the external driving microwave, expecting
“injection locking” effects22. The red curve in Fig. 3b exemplifies the emission power
spectrum at the hot spot when the external drive power Pdrivecorresponding to six
photons in the resonator (N* (Pdrive/0)/ 6) is applied. The driven emission (red
curve) reproduces the shape of the drive signal (blue curve) at frequency drive /2
(drive/2 = – 0.5 MHz), while the emission is suppressed at drive. This is
consistent with the expected locking mechanism of the emission. The red peak is also
much higher than the blue one which is the transmitted spectrum measured with the same
drive power and at /h = 40 GHz (outside the hot spots). We measured the injection
locking in the range of drive/2 from – 1.5 MHz to 0.5 MHz and found that locking
takes place at higher power for larger detuning from the emission peak maximum. The
spectrum strongly depends on Pdrive (Fig. 3c). When N* exceeds 1, the emission line
shrinks to the drive frequency with the width limited by the measurement bandwidth (100
kHz) and amplitude fluctuations in the locked signal are suppressed. The injection
locking effect resulting in frequency stabilization and emission narrowing additionally
proves the lasing action.
We have demonstrated a lasing effect in the simplest possible geometry – one
‘atom’ coupled to a resonator. The physical simplicity and controllability makes it
especially attractive for studying fundamental laser properties. We expect that the
artificial-atom masers can be used as on-chip microwave sources and microwave
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Acknowledgments We are grateful to A. Zagoskin, A. Smirnov, L. Murokh, S. Kouno, A. Tomita, and A.
Clerk for useful discussions.
Competing Interests The authors declare that they have no competing financial interests.
Correspondence Correspondence and requests for materials should be addressed to O. Astafiev
Figure 1 Single artificial-atom maser and lasing mechanism. a, Schematic
representation of the circuit. b, Scanning-electron micrograph of the qubit. The
Josephson charge qubit consists of a superconducting Al island, with the
charging energy EC = e2/2C = h 20 GHz (C is the total capacitance of the
island), connected to the ground through two Josephson junctions with a SQUID
geometry so that the effective Josephson energy EJ is controlled by a magnetic
flux through the loop. A voltage-biased drain electrode is connected to the
island via a 1.0-M tunnel junction. A tail of an Al strip (see also c) forms another
tunnel junction with estimated capacitance of Cr~ 200 aF, defining the qubit-
resonator coupling. The small junction conductance ~(200 k)-1 is irrelevant for
the unbiased junction. c, Micrograph of the left end of the Nb coplanar waveguide
resonator. At each end of the resonator, the central line is capacitively coupled to
the external microwave line with a characteristic impedance of 50 . The qubit is
fabricated close to the end of the ~ 6.24-mm long resonator. Bright stripes on top
of the SiO2 insulating layer are the qubit dc bias lines. An Al strip extends from
the resonator towards the qubit for realizing strong capacitive coupling. d, Energy
band diagram of the qubit (top right) and the lasing mechanism (bottom left). For
> 0, population inversion is created by two sequential single-electron tunnelling
events (|2 |1 |0) from the island to the drain.
Figure 2 Emission from the self-running maser. a, Transmission spectrum
through the resonator measured with a weak microwave power (P = –138 dBm)
as a function of the magnetic flux in the SQUID loop. The average number of
photons in the resonator is kept below 0.3. The detuning /2 ( - 0)/2 is
the difference between the probe frequency /2 and the resonator frequency
0/2 (= 9.899 GHz). The qubit is biased at = 0 and Vb= 0, so that the qubit
energy E equals to EJ and there is no current injection. The observed dispersion
curve is reproduced by
with EJ = EJ0
cos|/0| (where 0 is the flux quantum), EJ0/h = 13.7 GHz and g0 /h = 80 MHz
(red dashed lines). b, Emission power spectrum S from the resonator (upper
panel) together with the current I through the qubit (lower panel) as a function of
or ng. Population inversion mechanism due to the JQP process is now activated
with Vb= 0.65 mV. The Josephson energy of the qubit is reduced to EJ /h = 5.4
GHz by applying a magnetic flux = 0.38 0. The emission is seen as two “hot
spots”, and the corresponding current peaks appear on the right slope of the JQP
peak ( > 0). This double hot spot feature is reproduced around every charge
degeneracy point between |n and |n+2, periodically in ng. However, in another
sample with lower , we observed a single hot spot with lower emission power. c,
Emission power spectrum S at one of the hot spots taken at /h = 7 GHz (red
curve). The black curve is an eye-guide envelope of the emission peak. The
background level originates from the amplifier which has the noise temperature of
Figure 3 Microwave amplification and injection locking. a, Normalized power
(upper panel) and phase (lower panel) of the coherent radiation from the
resonator as a function of detuning of the driving microwave drive/2, off the hot
spots (blue, /h = 40 GHz) and at the hot spot (red, /h 7 GHz) with Vb= 0.65
mV. The amplitude is normalized to the input driving power of Pdrive= – 135 dBm
corresponding to N* = 0.6 at drive = 0. At drive/2 ~ – 0.6 MHz the
amplification regime switches to the attenuated transmission regime. The change
of the regimes is also seen as a sudden phase drop. b, Output power spectrum S
under the driving microwave field at a fixed detuning drive/2 = – 0.5 MHz and
with a power Pdrive = – 125 dBm. The blue curve is measured outside hot spots,
while the red curve is taken at the hot spot (/h 7 GHz). The black dashed curve
is the envelope of the emission spectrum in the absence of any microwave drive
(see Fig. 2c). c, Output power spectrum S (colour map in log scale) as a function
of the driving power for the detuning frequency drive/2 = – 0.5 MHz. The
spectrum gets as narrow as the measurement bandwidth (100 kHz) when N*
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