Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum (original) (raw)
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Generating “squeezed” superpositions of coherent states using photon addition and subtraction
2008
We study how photon addition and subtraction can be used to generate squeezed superpositions of coherent states in free-traveling fields (SSCSs) with high fidelities and large amplitudes. It is shown that an arbitrary N-photon subtraction results in the generation of a SSCS with nearly the perfect fidelity (F > 0.999) regardless of the number of photons subtracted. In this case, the amplitude of the SSCS increases as the number of the subtracted photons gets larger. For example, two-photon subtraction from a squeezed vacuum state of 6.1dB can generate a SSCS of α = 1.26, while in the case of the four-photon subtraction a SSCS of a larger amplitude α = 1.65 is obtained under the same condition. When a photon is subtracted from a squeezed vacuum state and another photon is added subsequently, a SSCS with a lower fidelity (F ≈ 0.96) yet higher amplitude (α ≈ 2) can be generated. We analyze some experimental imperfections including inefficiency of the detector used for the photon subtraction.
Quantum metrology of solid-state single-photon sources using photon-number-resolving detectors
New Journal of Physics
Quantum-light sources based on semiconductor quantum dots (QDs) are promising candidates for many applications in quantum photonics and quantum communication. Important emission characteristics of such emitters, namely the single-photon purity and photon indistinguishability, are usually assessed via time-correlated measurements using standard 'click' detectors in Hanbury Brown and Twiss or Hong-Ou-Mandel (HOM-) type configurations. In this work, we employ a state-of-theart photon-number-resolving (PNR) detection system based on superconducting transition-edge sensors (TESs) to directly access the photon-number distribution of deterministically fabricated solidstate single-photon sources. Offering quantum efficiencies close to unity and high energy resolution, our TES-based two-channel detector system allows us to analyse the quantum optical properties of a QD-based non-classical light source. In particular, it enables the direct observation of the two-particle Fock-state resulting from interference of quantum mechanically indistinguishable photons in HOMexperiments. Additionally, comparative measurements reveal excellent quantitative agreement of the photon-indistinguishabilities obtained with PNR ((90±7)%) and standard click ((90±5)%) detectors. Our work thus demonstrates that TES-based detectors are perfectly suitable for the quantum metrology of non-classical light sources and higlights appealing prospects for the efficient implementation of quantum information tasks based on multi-photon states.
Generation of a Superposition of Odd Photon Number States for Quantum Information Networks
Physical Review Letters, 2006
We report on the experimental observation of quantum-network-compatible light described by a non-positive Wigner function. The state is generated by photon subtraction from a squeezed vacuum state produced by a continuous wave optical parametric amplifier. Ideally, the state is a coherent superposition of odd photon number states, closely resembling a superposition of weak coherent states (a Schrödinger cat), with the leading contribution from a single photon state in the low parametric gain limit. Light is generated with about 10,000 and more events per second in a nearly perfect spatial mode with a Fourier-limited frequency bandwidth which matches well atomic quantum memory requirements. The generated state of light is an excellent input state for testing quantum memories, quantum repeaters and linear optics quantum computers. PACS numbers: 03.65.Wj; 03.67.-a; 42.50.Dv
Measuring the quantum nature of light with a single source and a single detector
Physical Review A, 2012
The introduction of light quanta by Einstein in 1905 triggered strong efforts to demonstrate the quantum properties of light 'directly', without involving matter quantization. It however took more than seven decades for the 'quantum granularity' of light to be observed in the fluorescence of single atoms 1. Single atoms emit photons one at a time, this is typically demonstrated with a Hanbury-Brown-Twiss setup 2 where light is split by a beam splitter and sent to two detectors resulting in anticorrelation of detected events. This setup, however, evokes the false impression that a beam splitter is necessary to prove indivisibility of photons. Here we show single-photon statistics from a quantum emitter with only one detector. The superconducting detector we fabricated has a dead time shorter 3 than the coherence time of the emitter. No beam splitter is employed, yet anticorrelations are observed. Our work significantly simplifies a widely used photon-correlation technique 4,5. A photon is a single excitation of a mode of the electromagnetic field. The probability P(n) to find exactly n excitations in the mode distinguishes different states of light. Figs. 1a and b show a schematic representation of a coherent state where P(n) is a Poissonian distribution together with a number (or Fock) state with exactly 1 photon per mode, respectively. In the case of a single-photon state (n=1) detection of a single excitation projects the measured mode to the vacuum state, i.e. the probability to detect another photon in the very same mode is zero. Since the temporal mode profile is associated with a characteristic coherence time τc, coincidence events within the time interval τc are absent, antibunching is observed. On the contrary, for a coherent state the probability to detect a second photon within the same mode is unchanged. Antibunching is thus not only a consequence of photons being indivisible particles but requires a specific quantum statistical distribution of discrete excitations. The latter requirement is overlooked in a simple classical explanation of antibunching in a Hanbury Brown and Twiss (HBT) experiment (Fig. 1c). There a photon is regarded as a classical indivisible particle and necessarily has to 'decide' which path to take when impinging on a beam splitter. Such an interpretation is too naïve 6 and even led to paradoxical conclusions, such as Wheeler's delayed choice paradox 7. Today, many different sources have been realized that generate antibunched light such as single-photon sources based on single atoms 8,9 , ions 10 , molecules 11,12 , colour centres 13 , or semiconductor quantum dots 14. Another approach utilizes quantum correlations between photon pairs to herald the presence of a single excitation in a specific mode 15. Photon statistics is typically measured in the above mentioned HBT setup. However, the only reason to use a beam splitter and two detectors is to circumvent the detector's dead time τd. For example, commercial avalanche photodiodes (APDs) have dead times of 50 ns-100 ns or longer, preventing the detection of coincidence events within the coherence time of typical single-photon sources which is on the order of a few nanoseconds. Although more recent experiments could generate single photons with coherence times up to several microseconds 16,17,18 HBT setups are still used.
Discrimination of optical coherent states using a photon number resolving detector
Journal of Modern Optics, 2010
The discrimination of non-orthogonal quantum states with reduced or without errors is a fundamental task in quantum measurement theory. In this work, we investigate a quantum measurement strategy capable of discriminating two coherent states probabilistically with significantly smaller error probabilities than can be obtained using non-probabilistic state discrimination. We find that appropriate postselection of the measurement data of a photon number resolving detector can be used to discriminate two coherent states with small error probability. We compare our new receiver to an optimal intermediate measurement between minimum error discrimination and unambiguous state discrimination.
Physical Review Letters, 2010
We experimentally demonstrate a new measurement scheme for the discrimination of two coherent states. The measurement scheme is based on a displacement operation followed by a photon number resolving detector, and we show that it outperforms the standard homodyne detector which we, in addition, proof to be optimal within all Gaussian operations including conditional dynamics. We also show that the non-Gaussian detector is superior to the homodyne detector in a continuous variable quantum key distribution scheme.
Self consistent, absolute calibration technique for photon number resolving detectors
Optics Express, 2011
Well characterized photon number resolving detectors are a requirement for many applications ranging from quantum information and quantum metrology to the foundations of quantum mechanics. This prompts the necessity for reliable calibration techniques at the single photon level. In this paper we propose an innovative absolute calibration technique for photon number resolving detectors, using a pulsed heralded photon source based on parametric down conversion. The technique, being absolute, does not require reference standards and is independent upon the performances of the heralding detector. The method provides the results of quantum efficiency for the heralded detector as a function of detected photon numbers. Furthermore, we prove its validity by performing the calibration of a Transition Edge Sensor based detector, a real photon number resolving detector that has recently demonstrated its effectiveness in various quantum information protocols. References and links 1. R. H. Hadfield, "Single-photon detectors for optical quantum information applications," Nature Photon. 3, 696-705 (2009) and ref.s therein. 2. C. Silberhorn, "Detecting quantum light," Contemp. Phys. 48, 143-156 (2007) and ref.s therein. 3. J. C. Zwinkels, E. Ikonen, N. P. Fox, G. Ulm, and M. L. Rastello, "Photometry, radiometry and 'the candela': evolution in the classical and quantum world," Metrologia 47, R15-R32 (2010). 4. Y. Gao, P. M. Anisimov, C. F. Wildfeuer, J. Luine, H. Lee, and J. P. Dowling, "Super-resolution at the shot-noise limit with coherent states and photon-number-resolving detectors," J.Opt. Soc. Am. B 27, A170-A174 (2010). 5. M. Genovese, "Research on hidden variable theories: A review of recent progresses," Phys. Rep. 413, 319-396 (2005) and ref.s therein. 6. G. Brida, M. Genovese, and I. Ruo Berchera, "Experimental realization of sub-shot-noise quantum imaging," Nature Photon. 4, 227-230 (2010). 7. T. Laenger, and G. Lenhart, "Standardization of quantum key distribution and the ETSI standardization initiative ISG-QKD," New J. Phys. 11, 055051 (2009) and ref.s therein. 8. J. L. O'Brien, A. Furusawa, and J. Vučković, "Photonic quantum technologies," Nature Photon. 3, 687-695 (2009) and ref.s therein. 9. N. Gisin and R. Thew, "Quantum communication," Nature Photon. 1, 165-171 (2007) and ref.s therein. 10. L. A. Jiang, E. A. Dauler, and J. T. Chang, "Photon-number-resolving detector with 10 bits of resolution," Phys. Rev. A 75, 062325 (2007). "Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum," Phys. Rev. A 82, 031802 (2010). 23. K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, "Sub-shot-noise-limit discrimination of on-off keyed coherent signals via a quantum receiver with a superconducting transition edge sensor," Opt. Express 18, 8107-8114 (2010). 24. A. Migdall, "Correlated-photon metrology without absolute standards," Phys. Today 52, 41-46 (1999) and ref.s therein. 25. G. Brida, M. Genovese, and M. Gramegna, "Twin-photon techniques for photo-detector calibration," Laser Physics Lett. 3, 115-123 (2006) and ref.s therein.
Seeing a single photon without destroying it
Nature, 1999
Light detection is usually a destructive process, in that detectors annihilate photons and convert them into electrical signals, making it impossible to see a single photon twice. But this limitation is not fundamentalÐquantum non-demolition strategies 1±3 permit repeated measurements of physically observable quantities, yielding identical results. For example, quantum non-demolition measurements of light intensity have been demonstrated 4±14 , suggesting possibilities for detecting weak forces and gravitational waves 3 . But such experiments, based on nonlinear optics, are sensitive only to macroscopic photon¯uxes. The non-destructive measurement of a single photon requires an extremely strong matter±radiation coupling; this can be realized in cavity quantum electrodynamics 15 , where the strength of the interaction between an atom and a photon can overwhelm all dissipative couplings to the environment. Here we report a cavity quantum electrodynamics experiment in which we detect a single photon non-destructively. We use atomic interferometry to measure the phase shift in an atomic wavefunction, caused by a cycle of photon absorption and emission. Our method amounts to a restricted quantum non-demolition measurement which can be applied only to states containing one or zero photons. It may lead to quantum logic gates 16 based on cavity quantum electrodynamics, and multi-atom entanglement 17 .
Physical Review A, 2012
We discuss a device capable of filtering out two-mode states of light with mode populations differing by more than a certain threshold, while not revealing which mode is more populated. It would allow engineering of macroscopic quantum states of light in a way which is preserving specific superpositions. As a result, it would enhance optical phase estimation with these states as well as distinguishability of "macroscopic" qubits. We propose an optical scheme, which is a relatively simple, albeit non-ideal, operational implementation of such a filter. It uses tapping of the original polarization two-mode field, with a polarization neutral beam splitter of low reflectivity. Next, the reflected beams are suitably interfered on a polarizing beam splitter. It is oriented such that it selects unbiased polarization modes with respect to the original ones. The more an incoming twomode Fock state is unequally populated, the more the polarizing beam splitter output modes are equally populated. This effect is especially pronounced for highly populated states. Additionally, for such states we expect strong population correlations between the original fields and the tapped one. Thus, after a photon-number measurement of the polarizing beam splitter outputs, a feedforward loop can be used to let through a shutter the field, which was transmitted by the tapping beam splitter. This happens only if the counts at the outputs are roughly equal. In such a case, the transmitted field differs strongly in occupation number of the two modes, while information on which mode is more populated is non-existent (a necessary condition for preserving superpositions).