Engineering nonlinear coherent states as photon-added and photon-subtracted coherent states (original) (raw)
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Physical Review A, 2010
We have created heralded coherent state superpositions (CSS), by subtracting up to three photons from a pulse of squeezed vacuum light. To produce such CSSs at a sufficient rate, we used our highefficiency photon-number-resolving transition edge sensor to detect the subtracted photons. This is the first experiment enabled by and utilizing the full photon-number-resolving capabilities of this detector. The CSS produced by three-photon subtraction had a mean photon number of 2.75 +0.06 −0.24 and a fidelity of 0.59 +0.04 −0.14 with an ideal CSS. This confirms that subtracting more photons results in higher-amplitude CSSs.
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.
Deformed photon-added nonlinear coherent states and their non-classical properties
Journal of Physics A: Mathematical and Theoretical, 2011
In this paper, we will try to present a general formalism for the construction of deformed photon-added nonlinear coherent states (DPANCSs) |α, f, m , which in special case lead to the well-known photon-added coherent state (PACS) |α, m. Some algebraic structures of the introduced DPANCSs are studied and particularly the resolution of the identity, as the most important property of generalized coherent states, is investigated. Meanwhile, it will be demonstrated that, the introduced states can also be classified in the f-deformed coherent states, with a special nonlinearity function. Next, we will show that, these states can be produced through a simple theoretical scheme. A discussion on the DPANCSs with negative values of m, i.e., |α, f, −m , is then presented. Our approach, has the potentiality to be used for the construction of a variety of new classes of DPANCSs, corresponding to any nonlinear oscillator with known nonlinearity function, as well as arbitrary solvable quantum system with known discrete, nondegenerate spectrum. Finally, after applying the formalism to a particular physical system known as Pöschl-Teller (P-T) potential and the nonlinear coherent states corresponding to a specific nonlinearity function f (n) = √ n, some of the nonclassical properties such as Mandel parameter, second order correlation function, in addition to first and second-order squeezing of the corresponding states will be investigated, numerically.
Generation of coherent states of photon-added type via pathway of eigenfunctions
Journal of Physics A: Mathematical and Theoretical, 2010
We obtain and investigate the regular eigenfunctions of simple differential operators x r d r+1 /dx r+1 , r = 1, 2, . . . with the eigenvalues equal to one. With the help of these eigenfunctions we construct a non-unitary analogue of boson displacement operator which will be acting on the vacuum. In this way we generate collective quantum states of the Fock space which are normalized and equipped with the resolution of unity with the positive weight functions that we obtain explicitly. These states are thus coherent states in the sense of Klauder. They span the truncated Fock space without first r lowest-lying basis states: |0 , |1 , . . . , |r − 1 . These states are squeezed, are sub-Poissonian in nature and are reminiscent of photon-added states at Agarwal et al.
Parametric Excitation of Photon-added Coherent States
Physica Scripta, 1998
We study the evolution of the photon-added coherent state o a, mT (introduced by Agarwal and Tara [Phys. Rev. A43, 492 (1991)]) due to a time dependence of the frequency of the electromagnetic Ðeld oscillator in a cavity or a vibrational frequency of an ion inside an electromagnetic trap. We give explicit expressions for the photon distribution function, mean values and variances of the quadrature components and of the photon number, the Wigner and Q-functions, etc. We show that the parametric excitation leads to strong oscillations of the photon (phonon) distribution function and changes the subpoissonian photon statistics to the superpoissonian one. Besides, it enables to achieve a larger squeezing coefficient than in the usual squeezed states.
2008
The operator annihilating a single quantum of excitation in a bosonic field is one of the cornerstones for the interpretation and prediction of the behavior of the microscopic quantum world. Here we present a systematic experimental study of the effects of single-photon annihilation on some paradigmatic light states. In particular, by demonstrating the invariance of coherent states by this operation, we provide the first direct verification of their definition as eigenstates of the photon annihilation operator.
Entropy
We present a concise review of recent experimental results concerning the conditional implementation of coherent superpositions of single-photon additions onto distinct field modes. Such a basic operation is seen to give rise to a wealth of interesting and useful effects, from the generation of a tunable degree of entanglement to the birth of peculiar correlations in the photon numbers and the quadratures of multimode, multiphoton, states of light. The experimental investigation of these properties will have an impact both on fundamental studies concerning, for example, the quantumness and entanglement of macroscopic states, and for possible applications in the realm of quantum-enhanced technologies.
Coherent states of nonlinear algebras: applications to quantum optics
Journal of Optics B: Quantum and Semiclassical Optics, 2000
We present a general unified approach for finding the coherent states of polynomially deformed algebras such as the quadratic and Higgs algebras, which are relevant for various multiphoton processes in quantum optics. We give a general procedure to map these deformed algebras to appropriate Lie algebras. This is used, for the non-compact cases, to obtain the annihilation operator eigenstates, by finding the canonical conjugates of these operators. Generalized coherent states, in the Perelomov sense, also follow from this construction. This allows us to explicitly construct coherent states associated with various quantum optical systems. *
Emergence of non-Gaussian coherent states through nonlinear interactions
Physical Review Research
Light-matter interactions that are nonlinear with respect to the photon number reveal the true quantum nature of coherent states. We characterize how coherent states depart from Gaussian by the emergence of negative values in their Wigner function during the evolution while maintaining their characteristic Poissonian photon statistics. Such states have non-minimum uncertainty yet present a metrological advantage that can reach the Heisenberg limit. Non-Gaussianity of light arises as a general property of nonlinear interactions, which only requires a polarizable media, resonant or dispersive. Our results highlight how useful quantum features can be extracted from the seemingly most classical states of light, a relevant phenomenon for quantum optics applications.
Perspectives for quantum state engineering via high nonlinearity in a double-EIT regime
Journal of Modern Optics, 2003
We analyse the possibilities for quantum state engineering offered by a model for Kerr-type nonlinearity enhanced by electromagnetically induced transparency (EIT), which was recently proposed by Petrosyan and Kurizki [Phys. Rev. A 65, 33833 (2002)]. We go beyond the semiclassical treatment and derive a quantum version of the model with both a full Hamiltonian approach and an analysis in terms of dressed states. The preparation of an entangled coherent state via a crossphase modulation effect is demonstrated. We briefly show that the violation of locality for such an entangled coherent state is robust against low detection efficiency. Finally, we investigate the possibility of a bi-chromatic photon blockade realized via the interaction of a low density beam of atoms with a bi-modal electromagnetic cavity which is externally driven. We show the effectiveness of the blockade effect even when more than a single atom is inside the cavity. The possibility to control two different cavity modes allows some insights into the generation of an entangled state of cavity modes.