Schrödinger-cat states of the electromagnetic field and multilevel atoms

Placing an ensemble of 10 6 ultracold atoms in the near field of a superconducting coplanar waveguide resonator (CPWR) with Q ∼ 10 6 one can achieve strong coupling between a single microwave photon in the CPWR and a collective hyperfine qubit state in the ensemble with g eff /2π ∼ 40 kHz larger than the cavity line width of κ/2π ∼ 7 kHz. Integrated on an atomchip such a system constitutes a hybrid quantum device, which also can be used to interconnect solid-state and atomic qubits, to study and control atomic motion via the microwave field, observe microwave super-radiance, build an integrated micro maser or even cool the resonator field via the atoms.PACS numbers: 42.50.Pq, 37.30.+i In the past decade important breakthroughs in implementing quantum information processing were reached in different physical implementations [1], each showing advantages and shortcomings. For quantum information to emerge as a valuable technology, it is mandatory to pool their strengths. Solid-state systems allow fast processing and dense integration; atom or ion based systems are slower but exhibit long qubit coherence times. Ensembles of atoms constitute a quantum memory, it can be read out onto photons [2] which can then be transmitted over long distances [3]. Here we analyze a device to quantum interconnect superconducting solid-state qubits to an atomic quantum memory.The challenge in transferring the state of a solidstate qubit to atoms is bridging the tremendous gap in time scales that govern solid-state and atomic physics devices. This difference can be overcome using a coplanar waveguide resonator (CPWR) [4,5,6], which can be electrically coupled to single superconducting qubits [7,8,9,10,11]. Various ways were proposed to couple to atomic and molecular systems [12,13,14,15,16,17,18]. The small effective mode volume together with the long photon lifetime allow a strong coupling.The superconducting qubit to CPWR coupling has been implemented and studied by several groups [7,8,9,10,11]. In this letter we concentrate on the magnetic coupling of a microwave photon in a CPWR to a collective hyperfine qubit in an ensemble of ultracold atoms. We show below that even though the magnetic coupling strength is much weaker than the optical dipole coupling, one can achieve strong coupling with currently available technology of circuit cavity quantum electro dynamics and ultracold atomic ensembles on an atomchip.As particular qubit example we consider a hyperfine transition in 87 Rb between |F = 2, m F and |F = 1, m F states which frequency of 6.83 GHz being ideally suited for a CPWR. In principle both systems can be integrated in a hybrid device on an single su- perconducting atomchip [19,20]. Besides the transfer of a single photon to the atomic ensemble as a quantum memory and back, such a hybrid quantum system opens up many different other possibilities. For example nondestructive microwave detection of the atomic density will allow to continuously monitor BEC formation or changing operating parameters one can achieve a superrad...

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“…For the internal dynamics of an ensemble of N atoms, we thus get an effective Hamiltonian in a standard Jaynes-Cummings form [29]:…”

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confidence: 99%

Strong Magnetic Coupling of an Ultracold Gas to a Superconducting Waveguide Cavity

et al. 2009

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“…By exploiting entangled quantum states, we can perform tasks that are otherwise difficult or impossible. Recently much attention has been focused on the entanglement of the field and atom in the Jaynes-Cummings (JC) model [1][2][3][4][5][6][7][8][9][10][11][12][13]. The authors in [1][2][3][4] have shown that entropy is a very useful operational measure of the entanglement degree of the quantum state, which automatically includes all moments of the density operator.…”

Section: Introductionmentioning

confidence: 99%

Entropy Growth and Degradation of Entanglement Due to Intrinsic Decoherence for an Initial Mixed State in the Multi-Quanta JC Model

Hessian

2008

Int J Theor Phys

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In this paper, we present a study of the entropy growth and degradation of entanglement due to intrinsic decoherence for some different initial states in the multi-quanta Jaynes-Cummings model. We analytically solve the Milburn equation for such JC model. Using an established entanglement measure based on the negativity of the eigenvalues of the partially transposed density matrix we find a very strong sensitivity of the maximally generated entanglement to the amount of decoherence, the multiplicity and the form of the and the initial state. Comparison with different measures of entanglement are made.

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“…Recently, much attention has been focused on the entanglement of the field and atom when the system starts from a pure state. [4][5][6][7][8][9][10][11][12][13][14][15][16] Also, in the context of the initial mixed state, some studies have been reported. [17][18][19][20] In this context, it has been shown that calculating the partial entropies of the field or the atom can be used as an operational measure of the entanglement degree of the generated quantum state.…”

Section: Introductionmentioning

confidence: 99%

“…1,9 From the identification and study of properties of such measures, further insight into the nature of entanglement is expected. In turn, their computation for particular states provide us with an account of the resources present in those states.…”

Section: Introductionmentioning

confidence: 99%

A Treatment of the Quantum Partial Entropies in the Atom-Field Interaction With a Class of Schrödinger Cat States

Obada

Hessian

Abdel‐Aty

2005

Int. J. Quantum Inform.

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This paper is an enquiry into the circumstances under which entropy and subentropy methods can give an answer to the question of quantum entanglement in the composite state. Using a general quantum dynamical system, we obtain the analytical solution when the atom initially starts from its excited state and the field in different initial states. Different features of the entanglement are investigated when the field is initially assumed to be in a coherent state, an even coherent state (Schrödinger cate state), and a statistical mixture of coherent states. Our results show that the setting of the initial state and the Stark shift play important roles in the evolution of the sub-entropies and entanglement.

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Schrödinger-cat states of the electromagnetic field and multilevel atoms

Cited by 70 publications

References 43 publications

Strong Magnetic Coupling of an Ultracold Gas to a Superconducting Waveguide Cavity

Strong Magnetic Coupling of an Ultracold Gas to a Superconducting Waveguide Cavity

Entropy Growth and Degradation of Entanglement Due to Intrinsic Decoherence for an Initial Mixed State in the Multi-Quanta JC Model

A Treatment of the Quantum Partial Entropies in the Atom-Field Interaction With a Class of Schrödinger Cat States

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