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arXiv:1503.08970 · Physical Review Letters

Optical Synthesis of Large-Amplitude Squeezed Coherent-State Superpositions with Minimal Resources

Kun Huang, Hanna Le Jeannic, Josselin Ruaudel, Varun Verma, Matthew D. Shaw, Francesco Marsili, S. W. Nam, E Wu, H. Zeng, Y.-C. Jeong, Radim Filip, Olivier Morin, Julien Laurat

Published Jul 9, 2015• 139 citations
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Abstract

We propose and experimentally realize a novel versatile protocol that allows the quantum state engineering of heralded optical coherent-state superpositions. This scheme relies on a two-mode squeezed state, linear mixing, and a n-photon detection. It is optimally using expensive non-Gaussian resources to build up only the key non-Gaussian part of the targeted state. In the experimental case of a two-photon detection based on high-efficiency superconducting nanowire single-photon detectors, the freely propagating state exhibits a 67% fidelity with a squeezed even coherent-state superposition with a size |α|(2)=3. The demonstrated procedure and the achieved rate will facilitate the use of such superpositions in subsequent protocols, including fundamental tests and optical hybrid quantum information implementations.

DOI
10.1103/physrevlett.115.023602

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We propose and experimentally realize a novel versatile protocol that allows the quantum state engineering of heralded optical coherent-state superpositions. This scheme relies on a two-mode squeezed state, linear mixing, and a n-photon detection. It is optimally using expensive non-Gaussian resources to build up only the key non-Gaussian part of the targeted state. In the experimental case of a two-photon detection based on high-efficiency superconducting nanowire single-photon detectors, the freely propagating state exhibits a 67% fidelity with a squeezed even coherent-state superposition with a size |α|(2)=3. The demonstrated procedure and the achieved rate will facilitate the use of such superpositions in subsequent protocols, including fundamental tests and optical hybrid quantum information implementations.
The generation of non-Gaussian quantum states is a key requirement for universal continuous-variable quantum information processing. We report the experimental generation of large-amplitude squeezed coherent-state superpositions (squeezed cat states) on free-space optical pulses, reaching an amplitude of α=2.47α= 2.47α=2.47, which, to our knowledge, exceeds all previously reported values. Our protocol relies on the controlled mixing of the Fock states ∣1⟩|1\rangle∣1⟩ and ∣2⟩|2\rangle∣2⟩ through a tunable beam splitter, followed by heralding via homodyne detection. The resulting state displays three well-resolved negative regions in its Wigner function and achieves a fidelity of 0.530.530.53 with the target state ∝S^(z)(∣α⟩−∣−α⟩)\propto \hat{S}(z)(|α\rangle - |-α\rangle)∝S^(z)(∣α⟩−∣−α⟩), with α=2.47α= 2.47α=2.47 and squeezing parameter z=0.56z = 0.56z=0.56. These results constitute a significant milestone for temporal breeding protocols and for the iterative generation of optical GKP states, opening new perspectives for scalable and fault-tolerant photonic quantum architectures.
The heralded optical parametric amplifier (OPA) has emerged as a promising tool for quantum state engineering. However, its potential has been limited to coherent state inputs. Here, we introduce a generalized heralded OPA protocol that unlocks a vastly expanded class of quantum phenomena by accepting arbitrary non-classical inputs. With a squeezed vacuum input, the setup functions as an integrated two-photon subtractor, deterministically generating high-fidelity, larger-amplitude squeezed Schrödinger cat states -- an operation previously requiring complex, discrete setups. Furthermore, when fed a small-amplitude SC state, the protocol acts as a non-Gaussianity amplifier, distilling it into high-purity approximations of key quantum resources like specific photon-number superpositions. This work transforms the OPA from a specialized source into a versatile and practical platform for advanced quantum state engineering, enabling the generation of a wide array of non-Gaussian states from a single, integrated setup.
The article shows that a single photon source and straightforward, purely optical processes can be used to produce a linear superposition of two macroscopically identifiable optical coherent states. A superposition of coherent states in a freely propagating optical field with high coherence amplitude can be generated via weak squeezing on a single photon, beam mixing with an auxiliary coherent state, and photon detection with imperfect threshold detectors. (α>2) and F=0.99, which is extremely precise. Our technique does not require a precise photon count, resolving measurements, or nonlinear Kerr-type interactions, in contrast to all existing schemes for obtaining such a state. It also exhibits some tolerance to inefficiencies in photon generation and is robust against detection of inefficiencies.
Optical Schrödinger cat states are non-Gaussian states with applications in quantum technologies, such as for building error-correcting states in quantum computing. Yet the efficient generation of high-fidelity optical Schrödinger cat states is an outstanding problem in quantum optics. Here, we propose using squeezed superpositions of zero and two photons, ∣θ⟩=cos⁡(θ/2)∣0⟩+sin⁡(θ/2)∣2⟩|θ\rangle = \cos{(θ/2)}|0\rangle + \sin{(θ/2)}|2\rangle∣θ⟩=cos(θ/2)∣0⟩+sin(θ/2)∣2⟩, as ingredients for protocols to efficiently generate high-fidelity cat states. We present a protocol using linear optics with success probability P≳50%P\gtrsim 50\%P≳50% that can generate cat states of size ∣α∣2=5|α|^2=5∣α∣2=5 with fidelity F>0.99F>0.99F>0.99. The protocol relies only on detecting single photons and is remarkably tolerant of loss, with 2%2\%2% detection loss still achieving F>0.98F>0.98F>0.98 for cats with ∣α∣2=5|α|^2=5∣α∣2=5. We also show that squeezed θθθ states are ideal candidates for nonlinear photon subtraction using a two-level system with near deterministic success probability and fidelity F>0.98F>0.98F>0.98 for cat states of size ∣α∣2=5|α|^2=5∣α∣2=5. Schemes for generating θθθ states using quantum emitters are also presented. Our protocols can be implemented with current state-of-the-art quantum optics experiments.
It is shown that a linear superposition of two macroscopically distinguishable optical coherent states can be generated using a single photon source and simple all-optical operations. Weak squeezing on a single photon, beam mixing with an auxiliary coherent state, and photon detecting with imperfect threshold detectors are enough to generate a coherent state superposition in a free propagating optical field with a large coherent amplitude $(\ensuremath{\alpha}>2)$ and high fidelity (F>0.99)(F>0.99)(F>0.99). In contrast to all previous schemes to generate such a state, our scheme does not need photon number resolving measurements nor Kerr-type nonlinear interactions. Furthermore, it is robust to detection inefficiency and exhibits some resilience to photon production inefficiency.