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Few-cycle vacuum squeezing in nanophotonics
Rajveer Nehra,
1
, Ryoto Sekine
1
,
, Luis Ledezma
1
,
2
,
Qiushi Guo
1
, Robert M. Gray
1
, Arkadev Roy
1
, and
Alireza Marandi
1
,
1
Department of Electrical Engineering,
California Institute of Technology, Pasadena, California 91125, USA.,
2
Jet Propulsion Laboratory,
California Institute of Technology, Pasadena, California 91109, USA.
These authors contributed equally to this work.
E-mail: marandi@caltech.edu, rnehra@caltech.edu
(Dated: January 19, 2022)
One of the most fundamental quantum states of light is squeezed vacuum, in which noise in one
of the quadratures is less than the standard quantum noise limit. Significant progress has been
made in the generation of optical squeezed vacuum and its utilization for numerous applications.
However, it remains challenging to generate, manipulate, and measure such quantum states in
nanophotonics with performances required for a wide range of scalable quantum information systems.
Here, we overcome this challenge in lithium niobate nanophotonics by utilizing ultrashort-pulse
phase-sensitive amplifiers for both generation and all-optical measurement of squeezed states on the
same chip. We generate a squeezed state spanning over more than 25 THz of bandwidth supporting
only a few optical cycles, and measure a maximum of 4.9 dB of squeezing (
11 dB inferred). This
level of squeezing surpasses the requirements for a wide range of quantum information systems.
Our results on generation and measurement of few-optical-cycle squeezed states in nanophotonics
enable a practical path towards scalable quantum information systems with THz clock rates and
open opportunities for studying non-classical nature of light in the sub-cycle regime.
Quantum information processing offers great
promises for computation, secure communication,
metrology and sensing. Many physical platforms
such as nuclear spins, superconducting circuits, pho-
tonics, trapped ions, quantum dots, and neutral
atoms have widely been explored in the pursuit to
build quantum information processors [1–6]. Among
these, photonics stands out because of its potential
for scalability, room-temperature logical operations,
and ease of encoding [7–11] quantum information in
both discrete [12] and continuous variables [13, 14].
In continuous-variable (CV) quantum photonics,
information is encoded in continuous amplitude
and phase values of the quantized electromagnetic
field.
The single-mode and multimode squeezed
states are widely used for various applications in-
cluding quantum-enhanced interferometry such as in
LIGO [15], microscopy [16], and quantum teleporta-
tion [17]. Moreover, highly entangled CV quantum
states, i.e., cluster states [7, 9, 10], serve as a univer-
sal resource for one-way quantum computation [18].
Typically, such high-quality CV states are gener-
ated from single or two-mode squeezed vacuum gen-
erated using quadratic (
χ
(2)
) parametric processes
either in bulk crystals or waveguides with large
(
100
μ
m
2
) mode areas [7–9, 19, 20]. While such
experiments using bulky discrete components have
been successful to demonstrate small and medium-
scale quantum circuits, it is highly desired to achieve
CV quantum states with comparable qualities in
nanophotonics to enable large-scale integrated quan-
tum circuits.
In nanophotonics, silicon nitride (SiN) and sil-
ica platforms have been used for many quantum
photonic experiments such as entangled photon-pair
generation, squeezing, error correction, and small
scale Gaussian boson sampling [21–25]. However,
their inherently weak cubic (
χ
(3)
) nonlinearity typi-
cally necessitates using high-Q resonators, which im-
poses limitations on accessible squeezing levels and
bandwidths. Despite significant advances, the mea-
sured squeezing levels have so far remained below 2
dB in nanophotonics [22, 23, 26, 27].
On the other hand, the measurements in CV
quantum systems have typically relied on balanced
homodyne detection (BHD) using highly-efficient
and low-noise photodetectors which are limited in
bandwidths to MHz and GHz ranges [28]. More-
over, in nanophotonics, the loss associated with
transferring the microscopic quantum states from a
tightly confined mode to a photodetector has im-
posed barriers in the measurement capabilities of
such states [22, 29–31]. A potential solution for these
measurement challenges lies in all-optical measure-
ment schemes based on a noiseless phase-sensitive
amplifier with sufficiently large gain [32–36] that can
eliminate the limitations of homodyne detection and
the sensitivity to detection losses. However, achiev-
arXiv:2201.06768v1 [quant-ph] 18 Jan 2022
2
Q
P
Amplified anti
-
squeezed
quadrature
Q
P
Q
P
Amplified squeezed
quadrature
Squeezed vacuum
b
c
Amplified shot
-
noise
Vacuum
d
Pump 2
Pump 1
Amplified squeezed vacuum
a
Squeezed
vacuum
Microscopic state
Macroscopic state
Macroscopic state
Pump
Signal
FIG. 1.
Illustration of generating squeezed vacuum and measuring it all optically in nanophotonics.
Phase-space distributions of
(a)
phase-quadrature squeezed vacuum, and its amplification in the
(b)
anti-squeezed
and
(c)
squeezed quadratures. The small (large) dashed circles correspond to shot-noise (amplified shot-noise level,
see text) and the small (large) filled ellipses are for squeezed vacuum (amplified squeezed vacuum).
d
) Sketch
of our nanophotonic device consisting of the Squeezer OPA, tapered adiabatic coupler, and Measurement OPA.
When pumped, the Squeezer OPA, generates a squeezed vacuum state, which is selectively coupled into an adjacent
waveguide. There, it is subsequently amplified by the Measurement OPA to macroscopic power levels.
ing such large gains (
>
30 dB) over broad optical
bandwidths is challenging in nanophotonics with cu-
bic nonlinearity [37].
Recently, lithium niobate (LN) nanophotonics has
opened promising avenues in optical communication,
sensing, and computation due to its extraordinary
optical, electrical, and acoustic properties [38, 39].
A combination of sub-wavelength confinement of the
optical mode, strong
χ
(2)
nonlinearity, high-fidelity
quasi-phasematching (QPM) by periodic poling, and
dispersion engineering for longer interaction lengths
has enabled devices outperforming the traditional
LN devices [40–43].
In this work, we use a nanophotonic circuit in LN
and experimentally demonstrate record-level genera-
tion and all-optical measurement of ultra-short-pulse
squeezed vacuum as the building block of a scal-
able CV quantum nanophotonics. Our circuit com-
bines two dispersion-engineered phase-sensitive op-
tical parametric amplifiers (OPAs) [40], as shown
in Fig. 1. The first OPA generates a microscopic
squeezed vacuum which is then amplified with a
high-gain OPA to macroscopic levels within the same
nanophotonic chip. The resulting macroscopic field
carries information about the microscopic squeezed
state, which can be measured with a high tolerance
to loss.
In Figure 1a, the phase-space distributions for vac-
uum (dashed circle) and phase-quadrature squeezed
vacuum (filled ellipse) are displayed. For the fig-
ure, we consider a particular case of 10-dB squeez-
ing with mean photon-number
N
sq-v
〉 ≈
2. The
squeezed light is then amplified by an OPA with 50
dB of phase-sensitive gain, thereby amplifying the
few-photon squeezed signal to a macroscopic power
level. In Fig. 1b and 1c, the phase-space distribu-
tions corresponding to amplified anti-squeezed and
amplified squeezed quadratures are shown for two
particular pump phases of the Measurement OPA,
φ
Pump 2
.
The dashed circles in Fig. 1b and 1c
3
represent the amplified shot-noise level correspond-
ing to the phase-space distribution of amplified vac-
uum. For brevity, we represent the distribution of
the amplified vacuum as a circle because the vacuum
state is phase-insensitive and therefore, the amplifi-
cation of any phase space quadrature by the Mea-
surement OPA will lead to the same noise level. In
the case of Fig. 1b with
φ
Pump 2
= 0, the anti-
squeezed quadrature (Q) is amplified while the or-
thogonal phase quadrature (P) is de-amplified such
that the output field is dominated entirely by the
Q quadrature and the P quadrature can be consid-
ered negligible. In such a high-gain amplification
regime, the total average photon-number (power) of
the output field is:
ˆ
N
+
〉∝〈
ˆ
Q
2
amp
〉≈O
(10
5
). Like-
wise, by changing the pump phase of the Measure-
ment OPA to
φ
Pump 2
=
π
, the original squeezed
quadrature is amplified to achieve
ˆ
N
〉∝〈
ˆ
P
2
amp
〉≈
O
(10
3
), as shown in Figure 1c. As a result, the
macroscopic output of the Measurement OPA pro-
vides a direct all-optical measurement of the micro-
scopic squeezed state. The squeezing (
S
) and anti-
squeezing (
S
+
) can then be determined as
S
±
[dB] =
10log
10
[
ˆ
N
±
/
ˆ
N
v
], where
ˆ
N
v
denotes the ampli-
fied vacuum. In the ideal case, the squeezing (anti-
squeezing) can be determined as [44]
S
±
[dB] = 10log
(
sinh
2
(
r
2
±
r
1
)
sinh
2
r
2
)
,
(1)
where
r
1
and
r
2
are the gain parameters for the
Squeezer and Measurement OPAs, respectively. Suf-
ficient gain (
>
33 dB for
11 dB of Squeezer OPA
gain, see Ref. [44], Part 6 for details) in the Mea-
surement OPA allows a direct measurement of the
phase-squeezed vacuum generated in the Squeezer
OPA [44]. Importantly, the high-gain Measurement
OPA makes our measurement tolerant to coupling
losses and photodetection inefficiencies as high as
7 dB [44].
In experiments, the Squeezer (low-gain) and
Measurement (high-gain) OPAs of our circuit are
periodically-poled with the lengths of 2.5 mm and
5.0 mm, respectively. The output of the Squeezer
OPA (microscopic squeezed vacuum) is coupled to
the Measurement OPA through a directional coupler.
To make our directional coupler broadband and less
susceptible to fabrication imperfections, we employ
an adiabatic design where both of the waveguides are
tapered while keeping the gap constant throughout
the coupler length. The coupler directs the squeezed
vacuum to the adjacent waveguide towards the Mea-
surement OPA, and keeps the residual pump of the
Squeezer OPA in the original waveguide as shown
in Fig. 1d. In our current device, the coupler causes
30% loss for the squeezed vacuum, and leaks
20%
of the squeezer pump to the Measurement OPA [44].
Our numerical simulations suggest that the coupling
performance can be significantly improved to
>
95%
for squeezed signal and
<
5% for squeezer pump,
which will lead to better measurement quality [44].
Our experimental setup is shown in Fig. 2a. The
Squeezer and Measurement OPAs are pumped by a
mode-locked laser (Menlo Systems Orange A) gener-
ating
75-fs-long nearly transform-limited pulses at
a 250-MHz repetition rate. The relative phase be-
tween Pump 1 (Squeezer OPA) and Pump 2 (Mea-
surement OPA) pulses is modulated by a piezoelec-
tric transducer (PZT) on the Pump 2 arm.
At
the output of the nanophotonic chip, the amplified
squeezed signal and Measurement OPA pump are
first separated using a dichroic mirror and then are
detected by two different optical spectrum analysers
(OSAs). In Fig. 2a, we show, (i) a false-colored
scanning electron microscope (SEM) image of our
nanophotonic circuit, (ii) a zoomed-in SEM image
of the coupler region, and (iii) a false-colored second
harmonic microscope image of the periodically-poled
region prior to etching the waveguides.
Figure 2b shows an example measurement of our
squeezed state. The green trace shows the output
signal of the Measurement OPA using an OSA in
a zero-span mode at 2090 nm while keeping both
Pump 1 and Pump 2 on and modulating the PZT
by a 1-Hz ramp signal. To accurately measure the
squeezing, we need to eliminate the effect of resid-
ual interference of the two pumps at the output of
the measurement. We achieve this by determining
the maximum and minimum of this residual inter-
ference and then calibrating our amplified shot-noise
levels by subsequently varying the power of Pump
2 to these maximum and minimum pump powers
while blocking Pump 1. These two levels of Pump
2 result in “shot-noise maximum” and “shot-noise
minimum” as shown in Fig. 2b, while “original shot-
noise” corresponds to the Pump 2 level during the
squeezing measurement. Hence, in the squeezing
measurement, the shaded area below (above) the
“shot-noise minimum” (“shot-noise maximum”) cor-
responds to squeezing (anti-squeezing) at the input
of the high-gain OPA. A detailed discussion on our
shot-noise calibration measurements can be found in
Ref. [44], Part 2.
We further characterize the dependence of squeez-
ing at 2090 nm on the pump power while keeping the
Pump 2 constant and performing the shot-noise cal-
ibration for each power level as shown in Fig. 2c. As
we increase the pump power in the Squeezer OPA,
the level of measured squeezing increases at first.
However, above 0.8 pJ of pump pulse energy, we ob-
4
Measurement
Amplifier Pump
Phase
Optical Power [dBm]
4.2 dB Squeezing
9.7 dB
Anti
-
Squeezing
b
c
d
TEC
Chip
Obj.
2090 nm
MLL
HWP
PBS
Delay
Stage
BS
Obj.
VND
1045 nm
a
DM
1
μ
m OSA
FC
2
μ
m OSA
PZT
Pump 1
Pump 2
e
5
μ
m
20
μ
m
Electrode finger
Domain wall
Z
Y
200
μ
m
(
i
)
(ii)
(iii)
FIG. 2.
Generation and measurement of squeezed light in the LN nanophotonic chip. a
) Experimental
setup. A MLL is split to pump the squeezer (Pump 1) and measurement (Pump 2) OPAs. The phase difference
between the pumps is modulated by a piezoelectric transducer (PZT) in the Pump 2 arm. At the output of the
nanophotonic chip, light from the measurement amplifier waveguide is collected. The amplified squeezed signal (red)
and residual Pump 2 (green) are separated using a DM, and measured by two different OSAs. (i) a false-colored
SEM image of our nanophotonic circuit, (ii) a zoomed-in SEM image of the coupler region, and (iii) a false-colored
second harmonic microscope image of the periodically-poled region prior to etching the waveguides.
b
) Squeezing
measurement by an OSA in the zero-span mode at 2090 nm. The green trace shows the amplified squeezed vacuum
when the PZT is modulated by a ramp signal. The other traces represent amplified vacuum (shot-noise) when Pump
1 is blocked at different Pump 2 powers (see main text).
c
) The squeezing measured at 2090 nm for several values of
Pump 1 while keeping Pump 2 constant.
d
) Loss analysis of the squeezing measurements. The solid (dashed) curves
show the degradation of anti-squeezing (squeezing) as the photon loss increases and the solid data points correspond
to measured values of minimum and maximum squeezing.
e
) The squeezer gain dependence on the energy of Pump 1.
Blue points are measured from anti-squeezing and red points are directly obtained from optical parametric generation
(OPG) measurements. Error bars are obtained from the statistics of the measurements. MLL: mode-locked laser,
PBS: polarized beamsplitter, BS: beam splitter, PZT: piezoelelectric transducer, HWP: half-wave plate, DM: dichroic
mirror, Obj.: reflective objective, VND: variable neutral-density filter, FC: fiber coupler, OSA: optical spectrum
analyzer, TEC: thermoelectric cooler.
serve that further increasing the squeezer pump de-
creases the level of measured squeezing. The degra-
dation of measured squeezing at high pump pow-
ers may be due to the existence of a small phase
noise and relative chirp between Pump 1 and Pump
2 which can mix the loss-degraded squeezed quadra-
ture with the relatively large anti-squeezed quadra-
ture [45, 46]. Additionally, parasitic nonlinear ef-
5
fects such as the photorefractive effect and nonlinear
absorption mechanisms in the waveguide can also
account for the degradation of squeezing at higher
pump powers.
Figure 2d shows how squeezing levels degrade in
the presence of photon loss (1
η
). The solid and
dashed curves represent anti-squeezing and squeez-
ing, respectively. Analytically,
S
±
[dB] = 10log[(1
η
) +
ηe
±
2
r
], where (1
η
) determines the loss
present in the detection protocol and
r
is the squeez-
ing parameter characterizing nonlinear interaction
strength [44]. The solid dots are the experimental
data points for the minimum and maximum amount
of measured squeezing at 2090 nm in Fig. 2c. From
these measurements, we estimate the total loss
L
=
1
η
0
.
3 experienced by the microscopic squeezed
signal before being fully amplified by the measure-
ment OPA. This agrees well with our measured cou-
pling efficiency of the adiabatic coupler using an aux-
iliary signal centered at 2090 nm (See Ref. [44], Part
4). From the fit, we infer that we successfully gen-
erated 10.6 dB of squeezing with the pump energy
of
<
1 pJ. This paves the way for fault-tolerant CV
quantum processors in LN nanophotonics, as 10.0
dB of squeezing is sufficient for many architectures
including recent proposals with Gottesman-Kitaev-
Preskill (GKP) qubit encodings [47, 48].
Figure 2e depicts the gain in the Squeezer OPA as
a function of Pump 1 pulse energy . The gain for
lower pump energies (
<
2.4 pJ) is determined from
the anti-squeezing measurements, while for higher
pump energies (
>
2.4 pJ) we obtain the gain from a
direct measurement of average photon-number [40,
44]. For a vacuum-seeded phase-sensitive OPA, the
average number of photons in the high parametric
gain regime (
ˆ
N
〉 ∼
G/
4) allows us to estimate the
gain [44]. The solid curve is the fit that includes the
overall detection efficiency (including off-chip cou-
pling losses and imperfect detection after the Mea-
surement OPA) and the nonlinear strength as fit-
ting parameters. From the fit, we extract the over-
all detection efficiency of
η
off-chip
overall
0
.
20 [44]. This
level of linear loss puts an upper limit of
<
1 dB
to the measurable squeezing for a standard BHD.
Remarkably, this is not a limiting factor for our
all-optical squeezing measurements because of the
noiseless amplification by the Measurement OPA.
Note that such lossy measurements are even more
detrimental for highly squeezed states, as they are
extremely sensitive to losses. This can be seen in
Fig. 2d, where
11 dB of initial squeezing degrades
by
10 dB in the presence of the detection losses
of
L
off-chip
overall
= 1
η
off-chip
overall
= 0
.
80. However, our
all-optical measurement is not affected by
L
off-chip
overall
losses due to the amplification by the Measurement
OPA and allows us to measure the squeezing levels
as high as 4.9 dB [44]. Thus, our measured squeezing
is mostly limited by the coupling losses at the adi-
abatic coupler, which can be fabricated with losses
of
<
0
.
05, as suggested by our numerical simula-
tions [44].
Figures 3a, 3b, and 3c show the measured squeez-
ing over a broad bandwidth. The amplified shot-
noise is calibrated using the same method as dis-
cussed earlier over the entire spectrum. Green traces
correspond to measurements by the OSA over three
different spectral windows when the PZT is modu-
lated by a slow ramp signal at 300 mHz. Squeez-
ing is present over the entire spectrum with a slight
spectral dependence. The measured squeezing is 3.8
dB around 1950 nm, 4.2 dB around 2090 nm, and
4.9 dB around 2200 nm. This is attributed to the
wavelength dependence of the coupling efficiency of
our adiabatic coupler [44]. We measured the squeez-
ing bandwidth to be 25.1 THz. The bandwidth is
expected to increase to 36.4 THz, as confirmed by
the optical parametric generation (OPG) from the
Squeezer OPA in Fig. 3d. The measured squeezing
bandwidth is mostly limited by the slight mismatch
of Measurement OPA gain in the wings of the spec-
trum, as evident from its OPG signal. Due to this
difference in the gain spectrum, the Measurement
OPA does not amplify the squeezed vacuum over
its entire generation bandwidth to macroscopic lev-
els, leading to a reduced measured squeezing band-
width. These measurements indicate that our gen-
erated squeezed state can occupy a record-level time
window of
4 optical cycles (See Ref. [44], Part
3), thereby opening many promising opportunities in
ultra-high-speed optical quantum information pro-
cessing.
Our results on generating and measuring squeezed
states all-optically in nanophotonics mark an im-
portant milestone for achieving scalable CV quan-
tum photonic systems. Figure 4 compares our mea-
sured squeezing and bandwidth with state-of-the-art
demonstrations in nanophotonic platforms including
SiN and Silica [44]. These experimental demonstra-
tions utilize relatively weaker
χ
(3)
nonlinearities and
require microresonators for enhancement. Addition-
ally, the squeezed light is typically detected using
off-chip BHDs which impose limitations on the mea-
sured squeezing (due to off-chip coupling losses) and
the accessible squeezing bandwidths. Our measured
squeezing substantially surpasses these other works
both in the magnitude and bandwidth.
In summary, we demonstrated few-cycle vacuum
squeezing in the LN nanophotonic platform. Our re-
sults represent a paradigm shift for on-chip squeezed