Andreas Nunnenkamp
ContactCavendish LaboratoryUniversity of Cambridge J. J. Thomson Avenue Cambridge, CB3 0HE United Kingdom

Research interests
 Cavity quantum optomechanics
 Superconducting circuits
 Topological qubits
 Ultracold atomic gases
My trajectory
 since 11/2014 Royal Society University Research Fellowship at Cavendish Laboratory, University of Cambridge
 09/2011  10/2014 Senior postdoctoral associate with Christoph Bruder at University of Basel, supported by the NCCR QSIT  Quantum Science and Technology
 10/2008  08/2011 Postdoctoral associate with Steve Girvin at Yale University
 10/2005  09/2008 Doctoral student with Keith Burnett at University of Oxford, supported by a Cecil Rhodes Scholarship
 01/2005  09/2005 Diploma student with Pierre Meystre at Optical Science Center, University of Arizona, Tucson, USA, supported by Studienstiftung des deutschen Volkes
 10/2002  12/2004 Graduate studies at University of Bonn, Germany, supported by Studienstiftung des deutschen Volkes
 08/2003  03/2004 Erasmus exchange student at Uppsala University, Sweden, supported by Studienstiftung des deutschen Volkes
 10/2000  09/2002 Undergraduate Studies at University of Bonn, Germany
Publications
Show all abstracts.1.  Detection of weak forces based on noiseactivated switching in bistable optomechanical systems 
Samuel Aldana, Christoph Bruder, and Andreas Nunnenkamp. Phys. Rev. A 90, 063810 (2014); arXiv:1409.8082.
We propose to use cavity optomechanical systems in the regime of optical bistability for the detection of weak harmonic forces. Due to the optomechanical coupling an external force on the mechanical oscillator modulates the resonance frequency of the cavity and consequently the switching rates between the two bistable branches. A large difference in the cavity output fields then leads to a strongly amplified homodyne signal. We determine the switching rates as a function of the cavity detuning from extensive numerical simulations of the stochastic master equation as appropriate for continuous homodyne detection. We develop a twostate rate equation model that quantitatively describes the slow switching dynamics. This model is solved analytically in the presence of a weak harmonic force to obtain approximate expressions for the power gain and signaltonoise ratio that we then compare to force detection with an optomechanical system in the linear regime.
 
2.  Quantum synchronization of two Van der Pol oscillators 
Stefan Walter, Andreas Nunnenkamp, and Christoph Bruder. Ann. Phys. 527, 131 (2015); arXiv:1406.7134.
We study synchronization of two dissipatively coupled Van der Pol oscillators in the quantum regime. Due to quantum noise strict frequency locking is absent and is replaced by a crossover from weak to strong frequency entrainment. We discuss the differences to the behavior of one quantum Van der Pol oscillator subject to an external drive. Moreover, we describe a possible experimental realization of two coupled quantum van der Pol oscillators in an optomechanical setting.
 
3.  Quantumlimited amplification and parametric instability in the reversed dissipation regime of cavity optomechanics 
A. Nunnenkamp, V. Sudhir, A. K. Feofanov, A. Roulet, and T. J. Kippenberg. Phys. Rev. Lett. 113, 023604 (2014); arXiv:1312.5867.
Cavity optomechanical phenomena, such as cooling, amplification, or optomechanically induced transparency, emerge due to a strong imbalance in the dissipation rates of the parametrically coupled electromagnetic and mechanical resonators. Here we analyze the reversed dissipation regime where the mechanical energy relaxation rate exceeds the energy decay rate of the electromagnetic cavity. We demonstrate that this regime allows for mechanically induced amplification (or cooling) of the electromagnetic mode. Gain, bandwidth, and added noise of this electromagnetic amplifier are derived and compared to amplification in the normal dissipation regime. In addition, we analyze the parametric instability, i.e., optomechanical Brillouin lasing, and contrast it to conventional optomechanical phonon lasing. Finally, we propose an experimental scheme that realizes the reversed dissipation regime using parametric coupling and optomechanical cooling with a second electromagnetic mode enabling quantumlimited amplification. Recent advances in highQ superconducting microwave resonators make the reversed dissipation regime experimentally realizable.
 
4.  Quantum synchronization of a driven selfsustained oscillator 
Stefan Walter, Andreas Nunnenkamp, and Christoph Bruder. Phys. Rev. Lett. 112, 094102 (2014); arXiv:1307.7044.
Synchronization is a universal phenomenon that is important both in fundamental studies and in technical applications. Here we investigate synchronization in the simplest quantummechanical scenario possible, i.e., a quantummechanical selfsustained oscillator coupled to an external harmonic drive. Using the power spectrum we analyze synchronization in terms of frequency entrainment and frequency locking in close analogy to the classical case. We show that there is a steplike crossover to a synchronized state as a function of the driving strength. In contrast to the classical case, there is a finite threshold value in driving. Quantum noise reduces the synchronized region and leads to a deviation from strict frequency locking.
 
5.  On the equivalence between an optomechanical system and a Kerr medium 
Samuel Aldana, Christoph Bruder, and Andreas Nunnenkamp. Phys. Rev. A 88, 043826 (2013); arXiv:1306.0415.
We study the optical bistability of an optomechanical system in which the position of a mechanical oscillator modulates the cavity frequency. The steadystate meanfield equation of the optical mode is identical to the one for a Kerr medium, and thus we expect it to have the same characteristic behavior with a lower, a middle, and an upper branch. However, the presence of position fluctuations of the mechanical resonator leads to a new feature: the upper branch will become unstable at sufficiently strong driving in certain parameter regimes. We identify the appropriate parameter regime for the upper branch to be stable, and we confirm, by numerical investigation of the quantum steady state, that the mechanical mode indeed acts as a Kerr nonlinearity for the optical mode in the lowtemperature limit. This equivalence of the optomechanical system and the Kerr medium will be important for future applications of cavity optomechanics in quantum nonlinear optics and quantum information science.
 
6.  Signatures of nonlinear cavity optomechanics in the weak coupling regime 
K. Borkje, A. Nunnenkamp, J. D. Teufel, and S. M. Girvin. Phys. Rev. Lett. 111, 053603 (2013); arXiv:1304.4155.
We identify signatures of the intrinsic nonlinear interaction between light and mechanical motion in cavity optomechanical systems. These signatures are observable even when the cavity linewidth exceeds the optomechanical coupling rate. A strong laser drive red detuned by twice the mechanical frequency from the cavity resonance frequency makes twophonon processes resonant, which leads to a nonlinear version of optomechanically induced transparency. This effect provides a new method of measuring the average phonon number of the mechanical oscillator. Furthermore, we show that if the strong laser drive is detuned by half the mechanical frequency, optomechanically induced transparency also occurs due to resonant twophoton processes. The cavity response to a second probe drive is in this case nonlinear in the probe power. These effects should be observable with optomechanical coupling strengths that have already been realized in experiments.
 
7.  Quantum limit of laser cooling in dispersively and dissipativelycoupled optomechanical systems 
Talitha Weiss and Andreas Nunnenkamp. Phys. Rev. A 88, 023850 (2013); arXiv:1304.2685.
Mechanical oscillators can be cooled by coupling them to an optical or microwave cavity. Going beyond the standard quantum noise approach, we find an analytic expression for the steadystate phonon number in systems where the position of the mechanical oscillator modulates the cavity frequency as well as the cavity linewidth. We trace the origin for the quantum limit of cooling to fluctuations in the optical force both at and away from the mechanical frequency. Finally, we calculate the minimal phonon number for the different types of couplings. Our study elucidates how to beneficially combine dispersive and dissipative optomechanical couplings.
 
8.  Microwavecontrolled coupling of Majorana bound states 
Thomas L. Schmidt, Andreas Nunnenkamp, and Christoph Bruder. New J. Phys. 15, 025043 (2013); arXiv:1302.4033.
We propose microwavecontrolled rotations for qubits realized as Majorana bound states. To this end, we study an inhomogeneous Kitaev chain in a microwave cavity. The chain consists of two topologically nontrivial regions separated by a topologically trivial, gapped region. The Majorana bound states at the interfaces between the left (right) regions and the central region are coupled, and their energies are split by virtual cotunneling processes. The amplitude for these cotunneling processes decreases exponentially with the number of sites of the gapped region, and the decay length diverges as the gap of the topologically trivial region closes. We demonstrate that microwave radiation can exponentially enhance the coupling between the Majorana bound states, both for classical and quantized electric fields. By solving the appropriate Liouville equation numerically, we show that microwaves can drive Rabi oscillations in the Majorana sector. Our model emerges as an effective description of a topological semiconductor nanowire in a microwave cavity. Thus, our proposal provides an experimentally feasible way to obtain full singlequbit control necessary for universal quantum computation with Majorana qubits.
 
9.  Strongcoupling effects in dissipatively coupled optomechanical systems 
Talitha Weiss, Christoph Bruder, and Andreas Nunnenkamp. New J. Phys. 15, 045017 (2013); arXiv:1211.7029.
In this paper we study cavity optomechanical systems in which the position of
a mechanical oscillator modulates both the resonance frequency (dispersive
coupling) and the linewidth (dissipative coupling) of a cavity mode. Using a
quantum noise approach we calculate the optical damping and the
opticallyinduced frequency shift. We find that dissipatively coupled systems
feature two parameter regions providing amplification and two parameter regions
providing cooling. To investigate the strongcoupling regime, we solve the
linearized equations of motion exactly and calculate the mechanical and optical
spectra. In addition to signatures of normalmode splitting that are similar to
the case of purely dispersive coupling, the spectra contain a striking feature
that we trace back to the Fano line shape of the force spectrum. Finally, we
show that purely dissipative coupling can lead to optomechanicallyinduced
transparency which will provide an experimentally convenient way to observe
normalmode splitting.
 
10.  Majorana qubit rotations in microwave cavities 
Thomas L. Schmidt, Andreas Nunnenkamp, and Christoph Bruder. Phys. Rev. Lett. 110, 107006 (2013); arXiv:1211.2201.
Majorana bound states have been proposed as building blocks for qubits on which certain operations can be performed in a topologically protected way using braiding. However, the set of these protected operations is not sufficient to realize universal quantum computing. We show that the electric field in a microwave cavity can induce Rabi oscillations between adjacent Majorana bound states. These oscillations can be used to implement an additional singlequbit gate. Supplemented with one braiding operation, this gate allows to perform arbitrary singlequbit operations.
 
11.  MeanField Analysis of Spinor Bosons in Optical Superlattices 
Andreas Wagner, Andreas Nunnenkamp, and Christoph Bruder. Phys. Rev. A 86, 023624 (2012); arXiv:1207.2911.
We study the groundstate phase diagram of spinless and spin1 bosons in optical superlattices using a BoseHubbard Hamiltonian that includes spindependent interactions. We decouple the unit cells of the superlattice via a meanfield approach and take into account the dynamics within the unit cell exactly. The system supports Mottinsulating as well as superfluid phases. The transitions between these phases are second order for spinless bosons and second or first order for spin1 bosons. Antiferromagnetic interactions energetically penalize highspin configurations and elongate all Mott lobes, especially the ones corresponding to an even atom number on each lattice site. We find that the quadratic Zeeman effect lifts the degeneracy between different polar superfluid phases leading to additional metastable phases and firstorder phase transitions. Finally, we show that an energy offset between the two sites of the unit cell induces a staircase of singleatom tunneling resonances, which surprisingly survives well into the superfluid regime.
 
12.  Cooling in the singlephoton strongcoupling regime of cavity optomechanics 
A. Nunnenkamp, K. Borkje, and S. M. Girvin. Phys. Rev. A 85, 051803(R) (2012); arXiv:1202.3263.
In this Rapid Communication we discuss how redsideband cooling is modified in the singlephoton strongcoupling regime of cavity optomechanics where the radiation pressure of a single photon displaces the mechanical oscillator by more than its zeropoint uncertainty. Using Fermi's golden rule we calculate the transition rates induced by the optical drive without linearizing the optomechanical interaction. In the resolvedsideband limit we find multiplephonon cooling resonances for strong singlephoton coupling that lead to nonthermal steady states including the possibility of phonon antibunching. Our study generalizes the standard linear cooling theory.
 
13.  Synthetic gauge fields and homodyne transmission in JaynesCummings lattices 
A. Nunnenkamp, Jens Koch, and S. M. Girvin. New J. Phys. 13, 095008 (2011); arXiv:1105.1817.
Manybody physics is traditionally concerned with systems of interacting
massive particles. Recent studies of effective interactions between photons,
induced in the circuit QED architecture by coupling the microwave field to
superconducting qubits, have paved the way for photonbased manybody physics.
We derive the magnitude and intrinsic signs of photon hopping amplitudes in
such circuit QED arrays. For a finite, ringshaped JaynesCummings lattice
exposed to a synthetic gauge field we show that degeneracies in the
singleexcitation spectrum emerge, which can give rise to strong correlations
for the interacting system with multiple excitations. We calculate the homodyne
transmission for such a device, explain the generalization of vacuum Rabi
splittings known for the singlesite JaynesCummings model, and identify
fingerprints of interactions beyond the linear response regime.
 
14.  Singlephoton Optomechanics 
A. Nunnenkamp, K. Borkje, and S. M. Girvin. Phys. Rev. Lett. 107, 063602 (2011); arXiv:1103.2788.
Optomechanics experiments are rapidly approaching the regime where the radiation pressure of a single photon displaces the mechanical oscillator by more than its zeropoint uncertainty. We show that in this limit the power spectrum has multiple sidebands and that the cavity response has several resonances in the resolvedsideband limit. Using masterequation simulations, we also study the crossover from the weakcoupling manyphoton to the singlephoton strongcoupling regime. Finally, we find nonGaussian steady states of the mechanical oscillator when multiphoton transitions are resonant. Our study provides the tools to detect and take advantage of this novel regime of optomechanics.
 
15.  Proposal for entangling remote micromechanical oscillators via optical measurements 
K. Borkje, A. Nunnenkamp, and S. M. Girvin. Phys. Rev. Lett. 107, 123601 (2011); arXiv:1103.2368.
We propose an experiment to create and verify entanglement between remote
mechanical objects by use of an optomechanical interferometer. Two optical
cavities, each coupled to a separate mechanical oscillator, are coherently
driven such that the oscillators are laser cooled to the quantum regime. The
entanglement is induced by optical measurement and comes about by combining the
output from the two cavities to erase whichpath information. It can be
verified through measurements of degrees of secondorder coherence of the
optical output field. The experiment is feasible in the regime of weak
optomechanical coupling. Realistic parameters for the membraneinthemiddle
geometry suggest entangled state lifetimes on the order of milliseconds.
 
16.  Superposition states of ultracold bosons in rotating rings with a weak potential barrier 
Andreas Nunnenkamp, Ana Maria Rey, and Keith Burnett. Phys. Rev. A 84, 053604 (2011); arXiv:1011.3444.
In a recent paper [Phys. Rev. A 82 063623 (2010)] Hallwood et al. argued that it is feasible to create large superposition states with strongly interacting bosons in rotating rings. Here we investigate in detail how the superposition states in rotatingring lattices depend on interaction strength and barrier height. With respect to the latter we find a tradeoff between energy gap and quality of the superposition state. Most importantly, we go beyond the deltafunction approximation for the barrier potential and show that the energy gap decreases exponentially with the number of particles for weak barrier potentials of finite width. These are crucial issues in the design of experiments to realize superposition states.
 
17.  Observability of radiation pressure shot noise in optomechanical systems 
K. Borkje, A. Nunnenkamp, B. M. Zwickl, C. Yang, J. G. E. Harris, and S. M. Girvin. Phys. Rev. A 82, 013818 (2010); arXiv:1004.3587.
We present a theoretical study of an experiment designed to detect radiation
pressure shot noise in an optomechanical system. Our model consists of a
coherently driven optical cavity mode that is coupled to a mechanical
oscillator. We examine the crosscorrelation between two quadratures of the
output field from the cavity. We determine under which circumstances radiation
pressure shot noise can be detected by a measurement of this crosscorrelation.
This is done in the general case of nonzero detuning between the frequency of
the drive and the cavity resonance frequency. We study the qualitative features
of the different contributions to the crosscorrelator and provide quantitative
figures of merit for the relative importance of the radiation pressure shot
noise contribution to other contributions. We also propose a modified setup of
this experiment relevant to the "membraneinthemiddle" geometry, which
potentially can avoid the problems of static bistability and classical noise in
the drive.
 
18.  Cooling and squeezing via quadratic optomechanical coupling 
A. Nunnenkamp, K. Borkje, J. G. E. Harris, and S. M. Girvin. Phys. Rev. A 82, 021806(R) (2010); arXiv:1004.2510.
We explore the physics of optomechanical systems in which an optical cavity
mode is coupled parametrically to the square of the position of a mechanical
oscillator. We derive an effective master equation describing twophonon
cooling of the mechanical oscillator. We show that for high temperatures and
weak coupling, the steadystate phonon number distribution is nonthermal
(Gaussian) and that even for strong cooling the mean phonon number remains
finite. Moreover, we demonstrate how to achieve mechanical squeezing by driving
the cavity with two beams. Finally, we calculate the optical output and
squeezing spectra. Implications for optomechanics experiments with the
membraneinthemiddle geometry or ultracold atoms in optical resonators are
discussed.
 
19.  Strong correlations in quantum vortex nucleation of ultracold atomic gases 
Andreas Nunnenkamp, Ana Maria Rey, and Keith Burnett. Proc. R. Soc. A (2010) 466, 12471263; arXiv:0911.4487.
We review some recent developments in the theory of rotating atomic gases.
These studies have thrown light on the process of nucleation of vortices in
regimes where meanfield methods are inadequate. In our review we shall
describe and compare quantum vortex nucleation of a dilute ultracold bosonic
gas trapped in three different configurations: a onedimensional ring lattice,
a onedimensional ring superlattice and a twodimensional asymmetric harmonic
trap. In all of them there is a critical rotation frequency, at which the
particles in the ground state exhibit strong quantum correlations. However, the
entanglement properties vary significantly from case to case. We explain these
differences by characterizing the intermediate states that participate in the
vortex nucleation process. Finally, we show that noise correlations are
sensitive to these differences. These new studies have, therefore, shown how
novel quantum states may be produced and probed in future experiments with
rotating neutral atom systems.
 
20.  Entanglement Metrology Using a Joint Readout of Superconducting Qubits 
J. M. Chow, L. DiCarlo, J. M. Gambetta, A. Nunnenkamp, Lev S. Bishop, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf. Phys. Rev. A 81, 062325 (2010); arXiv:0908.1955.
Accurate and precise detection of multiqubit entanglement is key for the
experimental development of quantum computation. Traditionally, nonclassical
correlations between entangled qubits are measured by counting coincidences
between singleshot readouts of individual qubits. We report entanglement
metrology using a single detection channel with direct access to
ensembleaveraged correlations between two superconducting qubits. Following
validation and calibration of this joint readout, we demonstrate full quantum
tomography on both separable and highlyentangled twoqubit states produced on
demand. Using a subset of the measurements required for full tomography, we
perform entanglement metrology with ~95% accuracy and ~98% precision despite
~10% fidelity of single measurements. For the highly entangled states, measured
ClauserHorneShimonyHolt operators reach a maximum value of 2.61+/0.04 and
entanglement witnesses give a lower bound of ~88% on concurrence. In its
present form, this detector will be able to resolve future improvements in the
production of twoqubit entanglement and is immediately extendable to 3 or 4
qubits.
 
21.  Proposal for generating and detecting multiqubit GHZ states in circuit QED 
Lev S. Bishop, L. Tornberg, D. Price, E. Ginossar, A. Nunnenkamp, A. A. Houck, J. M. Gambetta, Jens Koch, G. Johansson, S. M. Girvin, and R. J. Schoelkopf. New J. Phys. 11, 073040 (2009); arXiv:0902.0324.
We propose methods for the preparation and entanglement detection of
multiqubit GHZ states in circuit quantum electrodynamics. Using quantum
trajectory simulations appropriate for the situation of a weak continuous
measurement, we show that the joint dispersive readout of several qubits can be
utilized for the probabilistic production of highfidelity GHZ states. When
employing a nonlinear filter on the recorded homodyne signal, the selected
states are found to exhibit values of the BellMermin operator exceeding 2
under realistic conditions. We discuss the potential of the dispersive readout
to demonstrate a violation of the Mermin bound, and present a measurement
scheme avoiding the necessity for full detector tomography.
 
22.  Macroscopic superposition states in rotating ring lattices 
Andreas Nunnenkamp and Ana Maria Rey. Journal of Modern Optics 55, 3339 (2008); arXiv:0802.4309.
We investigate the effects of rotation on onedimensional ultracold bosons
confined to optical ring lattices. First, we show that there exists a critical
rotation frequency at which the ground state of a weaklyinteracting and
integerfilled atomic gas is fragmented into a macroscopic superposition state
with different circulation. Second, we point out several advantages of using
slightly nonuniform ring lattices. Finally, we demonstrate that different
quasimomentum states can be distinguished in timeofflight absorption imaging
and propose to probe correlations via the manybody oscillations induced by a
sudden change in the rotation frequency.
 
23.  Generation of macroscopic superposition states in ring superlattices 
Andreas Nunnenkamp, Ana Maria Rey, and Keith Burnett. Phys. Rev. A 77, 023622 (2008); arXiv:0711.3831.
Ultracold bosons in rotating ring lattices have previously been shown to form
macroscopic superpositions of different quasimomentum states. We demonstrate
that the generation of such kind of states using slightly nonuniform ring
lattices has several advantages: the energy gap decreases less severely with
the number of particles, the sensitivity to detunings from the critical
rotation frequency is reduced, and the scheme is not limited to commensurate
filling. We show that different quasimomentum states can be distinguished in
timeofflight absorption imaging and propose to probe correlations via the
manybody oscillations induced by a sudden change in the rotation frequency.
 
24.  Creation of resilient entangled states and a resource for measurementbased quantum computation with optical superlattices 
B. Vaucher, A. Nunnenkamp, and D. Jaksch. New J. Phys. 10, 023005 (2008); arXiv:0710.5099.
We investigate how to create entangled states of ultracold atoms trapped in
optical lattices by dynamically manipulating the shape of the lattice
potential. We consider an additional potential (the superlattice) that allows
both the splitting of each site into a double well potential, and the control
of the height of potential barrier between sites. We use superlattice
manipulations to perform entangling operations between neighbouring qubits
encoded on the Zeeman levels of the atoms without having to perform transfers
between the different vibrational states of the atoms. We show how to use
superlattices to engineer manybody entangled states resilient to collective
dephasing noise. Also, we present a method to realize a 2D resource for
measurementbased quantum computing via Bellpair measurements. We analyze
measurement networks that allow the execution of quantum algorithms while
maintaining the resilience properties of the system throughout the computation.
 
25.  Classical field techniques for condensates in onedimensional rings at finite temperatures 
A. Nunnenkamp, J. N. Milstein, and K. Burnett. Phys. Rev. A 75, 033604 (2007); condmat/0611645.
For a condensate in a onedimensional ring geometry, we compare the
thermodynamic properties of three conceptually different classical field
techniques: stochastic dynamics, microcanonical molecular dynamics, and the
classical field method. Starting from nonequilibrium initial conditions, all
three methods approach steady states whose distribution and correlation
functions are in excellent agreement with an exact evaluation of the partition
function in the hightemperature limit. Our study helps to establish these
various classical field techniques as powerful nonperturbative tools for
systems at finite temperatures.
 
26.  Full counting statistics of heteronuclear molecules from Feshbachassisted photo association 
A. Nunnenkamp, D. Meiser, and P. Meystre. New J. Phys. 8, 88 (2006); condmat/0508080.
We study the effects of quantum statistics on the counting statistics of
ultracold heteronuclear molecules formed by Feshbachassisted photoassociation
[Phys. Rev. Lett. {\bf 93}, 140405 (2004)]. Exploiting the formal similarities
with sum frequency generation and using quantum optics methods we consider the
cases where the molecules are formed from atoms out of two BoseEinstein
condensates, out of a BoseEinstein condensate and a gas of degenerate
fermions, and out of two degenerate Fermi gases with and without superfluidity.
Bosons are treated in a single mode approximation and fermions in a degenerate
model. In these approximations we can numerically solve the master equations
describing the system's dynamics and thus we find the full counting statistics
of the molecular modes. The full quantum dynamics calculations are complemented
by mean field calculations and short time perturbative expansions. While the
molecule production rates are very similar in all three cases at this level of
approximation, differences show up in the counting statistics of the molecular
fields. The intermediate field of closedchannel molecules is for short times
secondorder coherent if the molecules are formed from two BoseEinstein
condensates or a BoseFermi mixture. They show counting statistics similar to a
thermal field if formed from two normal Fermi gases. The coherence properties
of molecule formation in two superfluid Fermi gases are intermediate between
the two previous cases. In all cases the final field of deeplybound molecules
is found to be twice as noisy as that of the intermediate state. This is a
consequence of its coupling to the lossy optical cavity in our model, which
acts as an input port for quantum noise, much like the situation in an optical
beam splitter.
