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arXiv:quant-ph/0410210 · Physical Review Letters

Transfer of Nonclassical Properties from a Microscopic Superposition to Macroscopic Thermal States in the High Temperature Limit

Hyunseok Jeong, Timothy C. Ralph

Published Sep 5, 2006• 61 citations
arXivHTMLPDF

Abstract

We present several examples where prominent quantum properties are transferred from a microscopic superposition to thermal states at high temperatures. Our work is motivated by an analogy of Schrödinger's cat paradox, where the state corresponding to the virtual cat is a mixed thermal state with a large average photon number. Remarkably, quantum entanglement can be produced between thermal states with nearly the maximum Bell-inequality violation even when the temperatures of both modes approach infinity.

DOI
10.1103/physrevlett.97.100401

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We present several examples where prominent quantum properties are transferred from a microscopic superposition to thermal states at high temperatures. Our work is motivated by an analogy of Schrödinger's cat paradox, where the state corresponding to the virtual cat is a mixed thermal state with a large average photon number. Remarkably, quantum entanglement can be produced between thermal states with nearly the maximum Bell-inequality violation even when the temperatures of both modes approach infinity.
We investigate a more reasonable analogy of Schrodinger's cat paradox, where the state corresponding to the virtual cat is a mixed thermal state with a large average photon number. Several examples show that prominent quantum properties can be transferred from a microscopic superposition to a significantly mixed thermal state. Even when the temperature of the initial thermal state approaches infinity, quantum coherence between extremely mixed thermal states is produced with the maximum negativity of the Wigner functions and conspicuous interference patterns. Entanglement can also be produced under the same condition between extremely mixed thermal states with nearly the maximum Bell-inequality violation.
The observation of quantum phenomena often necessitates sufficiently pure states, a requirement that can be challenging to achieve. In this study, our goal is to prepare a nonclassical state originating from a mixed state, using dynamics that preserve the initial low purity of the state. We generate a quantum superposition of displaced thermal states within a microwave cavity using only unitary interactions with a transmon qubit. We measure the Wigner functions of these "hot" Schrödinger cat states for an initial purity as low as 0.06. This corresponds to a cavity mode temperature of up to 1.8 kelvin, 60 times hotter than the cavity's physical environment. Our realization of highly mixed quantum superposition states could be implemented with other continuous-variable systems, e.g., nanomechanical oscillators, for which ground-state cooling remains challenging.
Abstract In this chapter, the notion of quantum superposition of states is introduced through the example of a polarized photon. This brings out the novel feature that the state of the system depends on how the experiment is set up. The paradoxical consequences of quantum superposition, such as that a cat can be simultaneously dead and alive, are also discussed. This is the essence of the famous Schrödinger’s cat paradox. This description motivates another important consequence of quantum mechanical description of multiple objects; namely, their ability to exist in an entangled state. The properties of the two objects can remain entangled no matter how far away they are from each other and thus have the ability to influence each other. After discussing these aspects of quantum mechanics, the application of quantum entanglement to novel phenomena of quantum teleportation and quantum computing are presented.
In this chapter, the notion of quantum superposition of states is introduced through the example of a polarized photon. This brings out the novel feature that the state of the system depends on how the experiment is set up. The paradoxical consequences of quantum superposition, such as a cat can be simultaneously dead and alive, are also discussed. This is the essence of the famous Schrödinger’s cat paradox. This description motivates another important consequence of quantum mechanical description of the multiple objects, namely, their ability to exist in an entangled state. The properties of the two objects can remain entangled no matter how far away they are from each other and thus have the ability to influence each other. After discussing these aspects of quantum mechanics, the application of quantum entanglement to novel phenomena of quantum teleportation and quantum swapping are presented.
The `Schrödinger's cat' thought experiment highlights the counterintuitive facet of quantum theory that entanglement can exist between microscopic and macroscopic systems, producing a superposition of distinguishable states like the fictitious cat that is both alive and dead. The hallmark of entanglement is the detection of strong correlations between systems, for example by the violation of Bell's inequality. Using the CHSH variant of the Bell test, this violation has been observed with photons, atoms, solid state spins, and artificial atoms in superconducting circuits. For larger, more distinguishable states, the conflict between quantum predictions and our classical expectations is typically resolved due to the rapid onset of decoherence. To investigate this reconciliation, one can employ a superposition of coherent states in an oscillator, known as a cat state. In contrast to discrete systems, one can continuously vary the size of the prepared cat state and therefore its dependence on decoherence. Here we demonstrate and quantify entanglement between an artificial atom and a cat state in a cavity, which we call a `Bell-cat' state. We use a circuit QED architecture, high-fidelity measurements, and real-time feedback control to violate Bell's inequality without post-selection or corrections for measurement inefficiencies. Furthermore, we investigate the influence of decoherence by continuously varying the size of created Bell-cat states and characterize the entangled system by joint Wigner tomography. These techniques provide a toolset for quantum information processing with entangled qubits and resonators. While recent results have demonstrated a high level of control of such systems, this experiment demonstrates that information can be extracted efficiently and with high fidelity, a crucial requirement for quantum computing with resonators.